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Chapter 2: Q. 25 (page 198)

Suppose g(x), h(x), and j(x) are differentiable functions with the values of the function and its derivative given in the following table:


x g(x) h(x) j(x) g'(x) h'(x) f'(x)
-1 3 0 1 -1 -2 -2
0 2 3 0 -2 3 -2
1 0 -1 -2 -2 -2 -1
2 -2 -2 -3 -1 0 2
3 -3 0 1 0 1 2

f(x)=g(x)(h(x)+j(x)) find f'(2)

Short Answer

Expert verified

The value isf'(2)=1

Step by step solution

01

Given information

We are given a table

x g(x) h(x) j(x) g'(x) h'(x) f'(x)
-1 3 0 1 -1 -2 -2
0 2 3 0 -2 3 -2
1 0 -1 -2 -2 -2 -1
2 -2 -2 -3 -1 0 2
3 -3 0 1 0 1 2
02

Calculate

f'(x)=g'(x)[h(x)+j(x)]+g(x)[h'(x)+j(x)]f'(2)=g'(2)[h(2)+j(2)]+g(2)[h'(2)+j(2)]f'(2)=-1[-5]+(-2)[0+2]f'(2)=5-4f'(2)=1

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Most popular questions from this chapter

In Exercises 69–80, determine whether or not f is continuous and/or differentiable at the given value of x. If not, determine any left or right continuity or differentiability. For the last four functions, use graphs instead of the definition of the derivative.

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