Curve sketching calculus calculator
Does calculus play a role in curve sketching?
Calculus plays a much smaller part in curve sketching than is commonly believed; it is just one of the tools at our disposal. Example: Sketch the graph of y = x4 2x2 + 7. The Y intercept is readily found to be (0, 7). If x is large positive then y is large positive. If x is large negative then y is large positive.
What are some good things to check when sketching a curve?
Curve Sketching Good things to check: Domain Vertical asymptotes: lim x!a f(x) = 1 Intercepts: x = 0, f(x) = 0 Horizontal asymptotes and end behavior: lim x!1 f(x) Chapter 3.6: Sketching Graphs 3.6.1: Domain, Intercepts, and Asymptotes Curve Sketching Example: Sketch 2
How do you draw a graph without a calculator?
With a partner or two and without the use of a graphing calculator, attempt to sketch the graphs of the following functions. Pertinent aspects of the graph to include (include as many as you can): x-intercepts(?) f0 changes sign at each of these numbers p since f0( 2) p < 0, f0( 1) > 0, f0(1) < 0, and f0(2) > 0.
How do you find the stationary points of a curve?
At this point we will look at the derivative of x3 + x + 1 to determine the stationary points (if any) and the intervals in which the curve increases or decreases. dy Now dx = 3x2 + 1. This is always positive, which tells us that the curve is increasing everywhere. Therefore, there are no stationary points. 4.
[PDF File]Mathematics Learning Centre - The University of Sydney
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into the behaviour of the function and the shape of the graph. Also we used calculus judiciously. Calculus plays a much smaller part in curve sketching than is commonly believed; it is just one of the tools at our disposal. Example: Sketch the graph of y = x4 −2x2 +7. Solution: 1. The Y intercept is readily found to be (0,7). 2.
[PDF File]Curve Sketching Date Period - Kuta Software
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Kuta Software - Infinite Calculus Name_____ Curve Sketching Date_____ Period____ For each problem, find the: x and y intercepts, x-coordinates of the critical points, open intervals where the function is increasing and decreasing, x-coordinates of the inflection points, open intervals where the
[PDF File]Curve Sketching Practice
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Curve Sketching Practice With a partner or two and without the use of a graphing calculator, attempt to sketch the graphs of the following functions. Pertinent aspects of the graph to include (include as many as you can): asymptotes (vertical/horizontal) domain local extrema/regions of increase/decrease points of in ection/concavity x-intercepts(?)
[PDF File]Section 8: Curve Sketching - OpenTextBookStore
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We could have incorporated this concavity information when sketching the graph for the previous example, and indeed we can see the concavity reflected in the graph shown. Example. 5 Use information about the values of f ' and f '' to help graph . f ( ) = x 2/ 3. 1/3 3 2 f ′( ) = x −. This is undefined at x = 0. 4/3 9 2 f ′′( ) =− x −
[PDF File]Curve Sketching - University of British Columbia
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Chapter 3.6: Sketching Graphs 3.6.1: Domain, Intercepts, and Asymptotes Curve Sketching Example: Sketch 1 Review: nd the domain of the following function. f(x) = p 3 x2 ln(x + 1) ( 1;0) [ 0; p 3 i Where might you expect f(x) to have a vertical asymptote? What does the function look like nearby?
[PDF File]Curve Sketching with Calculus - Stanford University
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Curve Sketching with Calculus • First derivative and slope • Second derivative and concavity. First Derivative: Review As you will recall, the first derivative of a
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