
	Where results make sense

Topic: Second derivative test

Related Topics

First derivative test

Derivative

Concavity

Van der Waals equation

Ida Lupino

Finance

Management

Politics of Ethiopia

Coalition for Unity and Democracy

Adidas

1991

In the News (Wed 30 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	test.doc
		The TEST SECOnd command, tests the second derivative of the energy by finite difference of the forces.
		TEST NOCO WRITE command has to be performed on a single CPU and writes all the necessary data from memory to a file specified by UNIT keyword.
		TEST NOCO READ has the same parameters as WRITE, but the complete information is stored to the memory from the file for the number of steps specified with the STEP keyword.
	www.lobos.nih.gov /Charmm/c29b1/test.html (685 words)

	The Second Derivative Test
		At a local maximum the derivative goes from positive to zero to negative as you pass the point in the direction of increasing x (or, more precisely, it is not negative just to the left and is not positive just to the right--it could just be flat).
		At a local minimum the derivative goes from negative to zero to positive as you pass through the point.
		The statement of the test said quite clearly that if the second derivative is zero at the critical point then no conclusions can be drawn about the nature of the critical point.
	www.maths.abdn.ac.uk /~igc/tch/ma1002/appl/node20.html (480 words)

	index.html (Site not responding. Last check: 2007-10-09)
		Since the second derivative is also undefined at x = 0, we can't tell if the function has a local maximum there using the second derivative test.
		The derivative is never equal to zero or undefined in the domain 0 < x < e, which means there are no critical values and thus no local extrema.
		We can see from the sign of -Log[x] (the rest of the second derivative is positive) that this switches from positive to negative at x = 1, so we have concave up at 0 < x < 1 and concave down at 1 < x < e.
	www.richmond.edu /~lwibberl/math211/solve43 (651 words)

	Concavity and the Second Derivative Test - HMC Calculus Tutorial
		In this tutorial you will review how the second derivative of a function is related to the shape of its graph and how that information can be used to classify relative extreme values.
		The Second Derivative Test provides a means of classifying relative extreme values by using the sign of the second derivative at the critical number.
		The Second Derivative Test relates the concepts of critical points, extreme values, and concavity to give a very useful tool for determining whether a critical point on the graph of a function is a relative minimum or maximum.
	www.math.hmc.edu /calculus/tutorials/secondderiv (689 words)

	Maple Handout on the Second Derivative Test (Site not responding. Last check: 2007-10-09)
		Set the derivative equal to zero and solve for x to find the local maxima and local minima of the original function.
		Set the second derivative equal to zero and solve for x to find the inflection point of the original function.
		Find values of the second derivative on both sides of the x value from part 1.
	ellerbruch.nmu.edu /Maple/MapleHandouts/SecDerivTestHandout.html (328 words)

	DerivAndShape.html
		If the first derivative of a function is positive on an interval, then the function is increasing on that interval; if the the first derivative of a function is negative on an interval, then the function is decreasing on that interval.
		The Second Derivative Test has the advantage that often it is easier to compute f ''(c) and determine its sign than it is to determine where f ' is positive or negative.
		Note that since f is a polynomial function, its second derivative is continuous everywhere and the Second Derivative Test is applicable.
	dl.uncw.edu /digilib/mathematics/calculus/differentiation/freeze/DerivAndShape.html (780 words)

	Second Derivative Test
		The second method of determining the nature of stationary points is by using the second derivative.
		The first derivative test should also be used if it is tedious to find the second derivative.
		Hence, when the second derivative test yields zero, the point may not be a point of inflexion.
	library.thinkquest.org /C0110248/calculus/cartesec.htm (167 words)

	Concavity Test (Site not responding. Last check: 2007-10-09)
		Since a negative second derivative implies a decreasing first derivative, f′ is positive throughout (x-h,x), and negative throughout (x,x+h), for some neighborhood h.
		If both the first and second derivatives are 0, and the third is nonzero, the point is not a maximum or minimum.
		The second derivative attains a local minimum, as its first derivative is 0 and its second is positive.
	www.mathreference.com /ca,ctest.html (340 words)

	Second derivative test - Wikipedia, the free encyclopedia
		In calculus, a branch of mathematics, the second derivative test determines whether a given stationary point of a function is a maximum or a minimum.
		For a function of more than one variable, the second derivative test generalizes to a test based on the eigenvalues of the function's Hessian matrix at the stationary point.
		In particular, assuming that all second order partial derivatives of f are continuous on a neighbourhood of a stationary point x, then if the eigenvalues of the Hessian at x are all positive, then x is a local minimum.
	en.wikipedia.org /wiki/Second_derivative_test (243 words)

	MATH 1080 #6: FIRST AND SECOND DERIVATIVE PROPERTIES
		Using the First Derivative Test, x = 10 corresponds to a relative maximum and x = 60 corresponds to a relative minimum.
		Since the second derivative is the derivative of the first derivative, it will determine if the first derivative is increasing or decreasing.
		Since the second derivative changes sign through x = 35, this means that x = 35 corresponds to a point of inflection.
	www-math.cudenver.edu /~rbyrne/online/1080/108w6.htm (1025 words)

	Calculus World
		It is possible to find the behavior of a function using the derivative and second derivative.
		The first derivative test funds the intervals where the function is increasing or decreasing.
		Using the second derivative test, it is possible to find the concavity and minimums of a function
	home.earthlink.net /~sfmm84/calculus/derivativetests.html (404 words)

	Calculus Solution "tank" (Site not responding. Last check: 2007-10-09)
		To mimimize area using calculus, the first or second derivative test must be used.
		To use the first derivative test, draw the first derivative number line and find the intervals on which A' is positive and negative.
		To use the second derivative test, find the second derivative and evaluate it at 5.
	www.kent.k12.wa.us /pcpow/solutions/calculus/tank4/index.html (186 words)

	Second partial derivative test - Wikipedia, the free encyclopedia
		In mathematics, the second partial derivatives test is a method in multivariable calculus used to determine if a critical point (x, y) is a minimum, maximum or saddle point.
		This is rationalized because the function must on its trace along the xz-plane have its derivative equal to zero and the same is true for a trace on the yz-plane.
		Application of the second partial derivatives test is fairly straightforward and it is usually used as an all-purpose tool for identifying what the critical values of a function are, i.e.
	en.wikipedia.org /wiki/Second_partial_derivative_test (461 words)

	Introductory Calculus: Second Derivative Test (Site not responding. Last check: 2007-10-09)
		It can be shown that the second derivative is negative for x < 0 and positive for x > 0.
		In the second graph, tangent lines are drawn which are horizontal (reminder: lines which are horizontal have a slope of 0).
		A function possibly has a point of inflection at a point where the second derivative is exactly 0 (or as we shall see, at a point where the second derivative does not exist).
	www.algebralab.org /studyaids/studyaid.aspx?file=Calculus_7-6.xml (313 words)

	curvesketching.nb
		One needs to calculate the second derivative, f"(x), and solve for the values of x where either the numerator or denominator are 0.
		Since the curvature must be entirely in one direction or the other between adjacent inflection points, one can test the second derivative at any convenient point in that interval to identify whether the function is concave up or concave down there.
		This information can either be used to supplement the picture of the function one has formed using the First Derivative Test (using smooth curves rather than straight lines), or as the basis for the Second Derivative Test (using the critical values as the points of interest).
	www.people.vcu.edu /~ldwibber/mgmt212/curvesketching (817 words)

	Second Derivatives on Maple
		Using the Second Derivative Test for Local Maxima and Minima with Maple
		Since the second derivative of a function tells the concavity of that function, it can be useful in testing whether a critical point is a local maximum or minimum.
		Then we assign the second derivative to a procedure, so we can find values of that funtion from Maple.
	ellerbruch.nmu.edu /Maple/SecondDeriv.html (200 words)

	unitles6 (Site not responding. Last check: 2007-10-09)
		Students will learn about the second derivative test and be able to perform it.
		Students will be able to identify a graphs concavity at given points by looking at the graph and by using the second derivative test.
		Go through some of yesterdays homework problems using the second derivative test instead of the first derivative test at the board with the students.
	www.mste.uiuc.edu /courses/educ362sp04/folders/fischer/unitles6.htm (388 words)

	Visual Calculus / Graphs and Derivatives
		Two geometrical conditions and two conditions using the derivative and second derivative are used to make this definition.
		There are three quizzes that test the relationships between the graph of a function and information about its derivatives.
		Quiz on determining which graph is the graph of a function, its derivative and its 2nd derivatives.
	archives.math.utk.edu /visual.calculus/3/graphing.14/index.html (455 words)

	[No title]
		We will also use the second derivative test from Calculus 1 to verify that the computed result is indeed the optimal value of the function that we are interested in.
		First Derivative Test: Suppose p is a critical point of a continuous function f.
		Second Derivative Test: Suppose p is a critical point of a continuous function f.
	www.math.fsu.edu /~sachutha/MAT3930/lab11/lab11.doc (746 words)

	Using the Second Derivative I
		If the second derivative f''(x) is non-zero at a critical point x = a (that is a point where the first derivative is zero - f'(a) = 0) then the sign of the second derivative may be used to classify the point x = a as a local maximum or a local minimum.
		Suppose y = f(x) and f'(a) = 0 and the second derivative f"(x) is continuous about an interval centered at x = a.
		When there are many minima, the first and second derivative based tests alone can not say which the greatest or absolute minimum.
	whyslopes.com /Calculus-Introduction/4_Extrema_Second_Derivative_Test.html (538 words)

	The Second Derivative Test
		To determine whether the derivative is increasing, we take the second derivative.
		The by the first derivative test, the derivative is positive to the left of
		Similarly at a relative minimum the second derivative is positive.
	www.ltcconline.net /greenl/Courses/105/CurveSketching/SECTST.HTM (141 words)

	Math 134, Test 1 - Solutions (Site not responding. Last check: 2007-10-09)
		To maximize this function, take its derivative, R ' (r) = 3500 - 20r, and set it equal to zero.
		Find the x-coordinates of the critical points of f and, for each critical point x = a, use the Second Derivative Test to determine if f has a relative maximum or a relative minimum at x = a.
		This is indeed an inflection point of f, since the sign of the second derivative changes from the left (f '' (-1)
	www.math.uiuc.edu /~dcmurphy/math134/test1solns.html (890 words)

	Second Derivative Test
		Note: You must try this method first on the test, or you will get points taken off.
		If f"(a)=0, then this test is inconclusive, and we must use a different test to determine nature (like the graphing test).
		For examples using the second derivative test, please see the homework solutions.
	math.bu.edu /people/camijo/SecTest.html (86 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		Second derivative test: EMBED Equation.3 is negative.) At x = 4, we have a relative minimum.
		Second derivative test: EMBED Equation.3 is positive.) At x = 1, the second derivative changes sign.
		Second derivative test: EMBED Equation.3 is positive.) At x = 1, we have a relative maximum.
	personal.ecu.edu /williamsron/math2119/set12.doc (867 words)

	First Derivative Test
		The first derivative test is used to determine the nature of stationary points in an equation.
		The second method, the second derivative test, is explained on the next page.
		the derivative when x is slightly smaller and slightly larger than n).
	library.thinkquest.org /C0110248/calculus/cartefirst.htm (141 words)

	Graphing Using First and Second Derivatives
		In addition, it is important to label the distinct sign charts for the first and second derivatives in order to avoid unnecessary confusion of the following well-known facts and definitions.
		Here are instruction for establishing sign charts (number line) for the first and second derivatives.
		The point x=a determines an inflection point for function f if f is continuous at x=a, and the second derivative f'' is negative (-) for xa, or if f'' is positive (+) for x a.
	www.math.ucdavis.edu /~kouba/CalcOneDIRECTORY/graphingdirectory/Graphing.html (790 words)

	Method 08
		B) Express the derivative as a single fraction.
		derivative test fails or if the second derivative is
		3B) The second derivative is not a fraction.
	www.wellington.org /nandor/Calculus/methods/meth08.htm (412 words)

	Test 2 Answers- Winter, 1998 (Site not responding. Last check: 2007-10-09)
		Remember, when you are differentiating a quotient, say to yourself "the denominator squared under the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator."
		I verbalize it by "the derivative of e to a power is e to that power times the derivative of that power."
		Find the inflection points, that is points on the graph where the second derivative changes sign.
	oregonstate.edu /instruct/mth251/cq/t2answ98.html (916 words)

	ch53.nb
		In fact the notation for higher derivatives of f(x) is given by
		This is the content of second derivative test.
		Therefore, by setting the derivative to zero and solve it for x, x = -5 is the critical point.
	faculty.kirkwood.edu /asoemad/53.html (260 words)

Try your search on: Qwika (all wikis)