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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

Find if f(x)= 3j(x)-2h(x) Find f'(3)

Short Answer

Expert verified

The value isf'(3)=4

Step by step solution

01

Given information

We are given a table of values


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 are given

f(x)=3j(x)-2h(x)f'(x)=3j'(x)-2h'(x)f'(3)=3j'(3)-2h'(3)f'(3)=3(2)-2(1)f'(3)=4

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