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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Chapter
Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Find the two points on the curve y = x4 2x2 –x that have a common tangent line.

To determine

To find: The two points on the curve y=x42x2x that have a common tangent line.

Explanation

Obtain the derivative of y.

dydx=ddx(x42x2x)=4x412(2x21)1x11=4x34x1

Thus, the derivative of y is, dydx=4x34x1.

Let the two points (a,b) and (p,q) have a common tangent line on the curve.

The slope of the tangent at the points (a,b) and (p,q) is computed as follows,

dydx|(a,b)=dydx|(p,q)

4a34a1=4p34p1 (1)

a3a=p3pa(a21)=p(p21)

Since (a,b) and (p,q) are different points, a and p are not the same . That is, ap

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