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Topic: Curve sketching

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	MTH Introduction to Curve Sketching with Derivatives (Site not responding. Last check: 2007-10-24)
		Sketch a graph in which the derivative is positive and the second derivative is positive.
		Sketch a graph in which the derivative is negative and the second derivative is negative.
		Sketch a curve in which the second derivative changes from negative to positive.
	users.stlcc.edu /amosher/IntroCurveSketch.htm (326 words)

	Curve sketching
		When you are asked to sketch a curve, you need be able to draw a quick sketch of the curve, showing the main details (such as where the curve crosses the axes).
		You should be able to quickly sketch straight line graphs, from your knowlege that in the equation y = mx + c, m is the gradient and c where the graph crosses the y-axis.
		When asked to sketch a more complicated graph, there are a number of things that you should work out before drawing your sketch.
	www.projectalevel.co.uk /maths/curve.htm (442 words)

	Curve sketching (Site not responding. Last check: 2007-10-24)
		1, 2, 3, or 10, 20, 30) then curves that are close indicate regions in which the rate of change of the function is large, whereas curves that are far apart indicate regions in which the rate of change of the function is small.
		The number beside each curve is the value of the function to which it corresponds.
		The level curves corresponding to heights of 10 and 30 are thick, whereas those corresponding to heights of 0 and 20 are not.
	www.chass.utoronto.ca /~osborne/MathTutorial/SKE.HTM (1127 words)

	Curve Sketching Tutorial
		Curve sketching is another practical application of differential calculus.
		These are general guidelines for all curves, so each step may not always apply to all functions.
		Sketch the curve between the points, using the intervals of increase and decrease and intervals of concavity.
	www.nipissingu.ca /calculus/tutorials/curves.html (1457 words)

	Sketching a curve (Site not responding. Last check: 2007-10-24)
		Instead of adding individual points, however, you turn on Sketch Curve and drag in the viewports to sketch the curve.
		You can quickly draw many curves in succession this way by simply dragging from one place to another, then moving to a new position and dragging again.
		To exit Sketch curve mode, either turn it off from the Model menu, press Esc, or by selecting another manipulation tool.
	www.mindavenue.com /en/support/onlineHelp/04_mode8.htm (204 words)

	Applications to Curve Sketching
		The sign of the derivative can be used to determine where a function is monotonic, i.e., increasing or decreasing, without relying on a graph.
		It can be used to sketch a graph or to verify the correctness of a given graph.
		Sketching the graph: Since the function is a cubic polynomial with a positive leading coefficient, we know that it is very negative for large negative values and very positive for large positive values.
	oregonstate.edu /instruct/mth251/Juha/cq/Stage7/Lesson/signOfDerivative.1.html (335 words)

	6. More on Curve Sketching
		This section deals with curves which are NOT polynomials.
		It is important to understand these types of graphs so that we can interpret error messages when we are using computers to draw them.
		So we are ready to sketch the curve:
	www.intmath.com /AppsDiff/6_More.php (204 words)

	[No title] (Site not responding. Last check: 2007-10-24)
		Sketch the graph of the function f(x) defined by EMBED Equation.2 .
		Give a rough sketch of the function showing all asymptotes to the curve.
		Show that y = x — 6 is an asymptote to the curve EMBED Equation.2 8.
	home.btconnect.com /LHS/MA/yr13/17hw_curve_sketching.doc (484 words)

	Differentiation: curve sketching (Site not responding. Last check: 2007-10-24)
		Armed with knowledge about stationary points and points of inflexion, you're now in a good position to apply this knowledge to curve sketching problems.
		Curve sketching is something of an art-there aren't really cut-and-dried techniques for doing it, and your best asset is probably your intuition.
		Here is a checklist of things to consider when setting out to sketch a curve.
	metric.ma.ic.ac.uk /differentiation/applications/sketching (150 words)

	SparkNotes: Applications of the Derivative (AB): Curve Sketching
		SparkNotes: Applications of the Derivative (AB): Curve Sketching
		Home : Math & Science : Math Study Guides : Calculus AB : The Derivative : Curve Sketching
		The general procedure for curve sketching is based on the material learned in the last few sections.
	www.sparknotes.com /math/calcab/applicationsofthederivative/section8.rhtml (691 words)

	5. Curve Sketching
		It is important in this section to learn the basic shapes of each curve that you meet.
		You need to be able to sketch the curve, showing important features.
		Sketch the curve and show intercepts, maxima and minima and points of inflection:
	www.intmath.com /AppsDiff/5_CuSk.php (357 words)

	☞ reference - pump curve - pump curve online guide (Site not responding. Last check: 2007-10-24)
		Have you ever wondered how to read a pump curve or even what a pump curve is? The pump curve will tell you the performance...
		A pump curve (blower curve for gases) is incorporated into the calculation to...
		To select a proper pump for a particular application it is necessary to utilize the system curve and the pump performance curve...
	www.4-web-reference.info /curve/pump-curve.html (622 words)

	Mat210 Section 5.4 Additional Curve Sketching (Site not responding. Last check: 2007-10-24)
		It would seem that with the advent of the graphing calculator, sketching and analyzing graphs should be easier and more efficient than ever before.
		Then sketch a graph of the function by hand on a piece of grid paper.
		Use the limit at infinity to sketch the end behavior of the graph and sketch any horizontal asymptotes.
	fym.la.asu.edu /~fym/mat210_web/lessons/Ch5/5_4/5_4ol.htm (723 words)

	sketching - Art collections - find the art you desire.
		Written by Paul Bourke June 1990 A somewhat unusual attempt at computer sketching is to attach a pen to a plotter loosely with Creativity (creative) Tools and Techniques - Brain sketching Creativity tools and techniques - Brain sketching.Deep Sky - Sketching and Observing Gallery of sketches, links, and sketches upload area..
		Written by Paul Bourke June 1990 A somewhat unusual attempt at computer sketching is to attach a pen to a plotter loosely with Nature journal and tree drawing tutorial focusing on tree silhouettes, limbs, leaves, seasonal deciduous trees, and evergreen trees.Graph Sketching and Recognition Graph Sketching and Recognition.
		Written by Paul Bourke June 1990 A somewhat unusual attempt at computer sketching is to attach a pen to a plotter loosely with
	www.artworksnj.org /art/sketching.html (854 words)

	3.5 Issues in Curve Sketching
		The first and second derivatives are used to sketch a curve by hand.
		The definitions of concepts connected with curve sketching.
		Use the slider to move the point P along the curve.
	www.math.dartmouth.edu /~klbooksite/3.05/305.html (336 words)

	Calculus I Web Sites, Ch. 3
		CURVE SKETCHING by Ziad Diab, Southwest Texas State University. Uses the tools from calculus to aid in sketching the curve: first derivative, second derivative, asymptotes.
		Curve Sketching by M. Bourne. Nice site with lots of graphs to illustrate how to use the tools of calculus.
		Full Curve Sketching by William A. Bogley and Robby Robson, Oregon State University. Discussion of curve sketching employing asymptotes, continuity, critical points.
	www.cedarville.edu /academics/sciencemath/lee/calculus/calc1-ch3-websites.htm (355 words)

	curve sketching (Site not responding. Last check: 2007-10-24)
		Sketch the following curves, indicating maximum and minimum points and points of inflection.
		Sketch a smooth curve illustrating the following characteristics or properties:
		to get each of the three types of curves illustrated.
	www.pen.k12.va.us /Div/Winchester/jhhs/math/lessons/calculus/crvskrev.html (105 words)

	Example of Analytical Curve Sketching (Site not responding. Last check: 2007-10-24)
		An inflection point on the original curve may occur at this x-value.
		Changes of concavity may also occur at the vertical asymptotes.
		The graph is likely slightly turning upward to the line but it is so faint our eyes and the software can not see it.
	users.stlcc.edu /amosher/CurveSketchAnalytical.htm (243 words)

	An Introduction to Curve Sketching (Site not responding. Last check: 2007-10-24)
		Every point can also be referred to, however, by its polar co-ordinates, by specifying the length of the line from your point to the origin, and the angle this line makes with the positive x-axis.
		This presentation looks at polar co-ordinates, and how equations using them can describe different curves.
		It also looks at curves traced out by a point on a disc rolling on a surface, then on and within another disc.
	www.maths.liv.ac.uk /~mathsclub/Topics/Curves (108 words)

	CopyCAD Includes New Curve Sketching and Editing Tools (Site not responding. Last check: 2007-10-24)
		Delcam has introduced a new version of its CopyCAD reverse engineering software that offers faster and more accurate alignment of multiple scans, together with new curve creation and editing tools for easier surfacing, and improvements to its abilities to develop horizon lines and to fill any gaps in the scanned data.
		The new curve creation options make sketching of wireframe geometry much easier, both in cases where the curves will be used as construction geometry and when they will be used to divide the model into regions for rapid surface creation.
		The software can also snap the curve back to the surface of the scan data automatically if the editing option would have lifted it away from the model.
	www.engineersedge.com /technology_news/posts/8.html (704 words)

	Curve Sketching (Site not responding. Last check: 2007-10-24)
		Suggestions for sketching the graph of a function
		Sketch the graph, paying close to where the function increases or decreases and is concave up or concave down.
		Then graph it in your calculator to see if you are correct.
	www.mecca.org /~halfacre/MATH/lesson22.htm (116 words)

	3D Buzz - Calculus: Curve Sketching
		I have a calculus test tomorrow on curve sketching.
		I have to know how to find the asymptotes, max/min pts, pt of inflection and then sketch it...
		If you want to make your sketch even more accurate add the other points you solved for while doing work on the problem.
	www.3dbuzz.com /vbforum/printthread.php?t=98565 (1332 words)

	Curve Sketching
		Firstly, let us construct a table of values for y = f(x) and
		Hence, we see that for the same value of x, the point on the curve
		Hence, we see that a point on the curve
	chuwm.tripod.com /curve/curve.html (331 words)

	Class EDU.emporia.mathtools.ParametricCurve
		The minimum suggested t-value to be used in sketching the curve
		The maximum suggested value of t that to be used in parameterizing the curve
		The minimum suggested value of t that to be used in parameterizing the curve
	www.joma.org /images/upload_library/4/vol1/toolkitjava/JOMA/javadocs/mathtoolkit/EDU.emporia.mathtools.ParametricCurve.html (583 words)

	Calculus@Internet
		Applications to Curve Sketching - Two examples of the applications of sketching a derived graph
		Full Curve Sketching - How to sketch graphs using differentiation and examples.
		Sketching (x - 1)/(x^2 - 4) - How to sketch the curve of (x - 1)/(x^2 - 4) using diffentiative techniques
	www.calculus.net /ci2/search/?request=category&code=123&off=0&tag=9200438920658 (364 words)

	☞ reference - altoona curve baseball schedule - altoona curve baseball schedule online guide (Site not responding. Last check: 2007-10-24)
		Blair County Ballpark: Altoona, PA: Altoona Curve: Hoover Metropolitan...
		Huntingdon Borough has received the Altoona Curve Baseball tickets and they are now available.
		The Altoona Curve baseball club is into its eighth season of Eastern League action as the Pittsburgh Pirates' Double-A affiliate.
	www.reference-101.info /curve/altoona-curve-baseball-schedule.html (232 words)

	Differentiation: curve sketching activity (Site not responding. Last check: 2007-10-24)
		For each of the following curves, produce a careful sketch using pen and paper.
		Your sketch should show, where possible, the points of intersection with the two axes, together with any stationary points and points of inflexion.
		After each sketch, check your work using the TangentDrag applet.
	metric.ma.ic.ac.uk /differentiation/applications/sketching/exploration/index.html (87 words)

	BBC Education - AS Guru - Maths - Pure - Functions - Curve Sketching
		BBC Education - AS Guru - Maths - Pure - Functions - Curve Sketching
		The key points in a graph sketch are:
		In this lesson we will look at these properties of graphs for a range of different functions.
	www.bbc.co.uk /education/asguru/maths/13pure/02functions/12curves (123 words)

	MATH 1401 #14: LIMITS AT INFINITY AGAIN - CURVE SKETCHING
		Use the fact that -1 < cos x < 1 to bound the function between two functions
		The following is a list of the steps in sketching the graph of a function by hand.
		Sketch by hand the graph of x e
	www-math.cudenver.edu /~rbyrne/online/140w14.htm (579 words)

	Calculus@Internet
		Origin and Derivation of the Derivative - To get things going I will explain a concept that is infrequenty taught in college, but is (I believe) necessary to understand what calculus is and where it comes from.
		The Derivative - The Slope Of a Curve:
		Rates of change and the slope of a curve - To see another way in which the derivative appears let's go back to our earlier discussion about making measurements
	www.calculus.net /ci2/search/?request=category&code=1231&off=0&tag=9200438920658 (321 words)

	BBC - Education Scotland - Higher Bitesize Revision - Maths - Calculus - Differentiation: Revision 9
		When you've found the stationary points and where the graph crosses the x- and y- axes, you can sketch the curve.
		Do the easy bit first and find where it crosses the y-axis.
		Now put together all the information we have found, and you have enough to sketch the curve.
	www.bbc.co.uk /scotland/education/bitesize/higher/maths/calculus/differentiation9_rev.shtml (140 words)

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