   Chapter 4.3, Problem 75E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# (a) If the function f(x) = x3 + ax2 + bx has the local minimum value − 2 9 3 at x = 1 / 3 , what are the values of a and b?(b) Which of the tangent lines to the curve in part (a) has the smallest slope?

(a)

To determine

To find: The values of a and b if the function f(x)=x3+ax2+bx has local minimum f(13)=293 .

Explanation

The function f(x)=x3+ax2+bx has local minimum is 293 at the point x=13 .

Substitute x=13 this in given function.

f(13)=(13)3+a(13)2+b(13)=293133+a3+b3=2931+3a+3b33=2931+3a+3b=2

3a+3b=3 (1)

If f has local minimum at x=13 then the derivative of the function at that point is zero That is f(13)=0

Obtain derivative of f(x)

(b)

To determine

To Find: The tangent line of the curve f(x)=x3+ax2+bx have smallest slope.

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 