Famous Curve The graph of the pear-shaped quartic b?y? = x°(a – x), a, b > 0 %3D is shown above. (a) Explain how you could use a graphing utility to graph this curve. (b) Use a graphing utility to graph the curve for various values of the constants a and b. Describe how a and b affect the shape of the curve. (c) Determine the points on the curve at which the tangent line is horizontal.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 20E
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Famous Curve The graph of the pear-shaped quartic
b?y? = x°(a – x), a, b > 0
%3D
is shown above.
(a) Explain how you could use a graphing utility to graph this
curve.
(b) Use a graphing utility to graph the curve for various values
of the constants a and b. Describe how a and b affect the
shape of the curve.
(c) Determine the points on the curve at which the tangent line
is horizontal.
Transcribed Image Text:Famous Curve The graph of the pear-shaped quartic b?y? = x°(a – x), a, b > 0 %3D is shown above. (a) Explain how you could use a graphing utility to graph this curve. (b) Use a graphing utility to graph the curve for various values of the constants a and b. Describe how a and b affect the shape of the curve. (c) Determine the points on the curve at which the tangent line is horizontal.
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