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Chapter 2: Q. 24 (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) j'(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

Calculate if f(x)=g(x)h(x) then find f'(0)

Short Answer

Expert verified

The answer isf'(0)=12

Step by step solution

01

Given information

We are given a table

x g(x) h(x) j(x) g'(x) h'(x) j'(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

We have,

f(x)=g(x)h(x)f'(x)=g(x)h'(x)+g'(x)h(x)f'(0)=2(3)-(-2)(3)f'(0)=6+6f'(0)=12

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