Question

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

The value is$f\text{'}\left(3\right)=4$

Step-by-step solution

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

Calculate

We are given

$$\begin{gathered} f\left(x\right)=3j\left(x\right)-2h\left(x\right) \\ f\text{'}\left(x\right)=3j\text{'}\left(x\right)-2h\text{'}\left(x\right) \\ f\text{'}\left(3\right)=3j\text{'}\left(3\right)-2h\text{'}\left(3\right) \\ f\text{'}\left(3\right)=3\left(2\right)-2\left(1\right) \\ f\text{'}\left(3\right)=4 \end{gathered}$$