Question

If h(x)= 7+4f(x), where f(2)=5 and (2)=9, find h'(2).

Answer 1

To find h'(2), use the chain rule and the given information about f(x) and f'(x).

Step-by-step explanation:

In order to find the derivative h'(2), we need to use the chain rule. Given that h(x) = 7 + 4f(x), we can rewrite the equation as h(x) = 7 + 4f(2), since we know f(2) = 5. We also need f'(2), which can be found using the given information that f'(2) = 9. Using the chain rule, the derivative of h(x) is h'(x) = 4f'(x).

Now, substituting x = 2, we have h'(2) = 4f'(2) = 4 * 9 = 36.