Question

AP Calc: Please explain how to find derivatives in function graphs of this problem, thanks.

Answer 1

C

Explanation:

First you have to find h'(x). To find it you have to use the multiplication differentiation rule. Therefore h'(x) is...

h'(x) = f(x)g'(x) + g(x)f'(x)

Then plug 2 into the equation

h'(2) = f(2)g'(2) +g(2)f'(2)

Then you use the graphs to find out the numerals for the equation

f(2) = 4

g(2) = 5

To find the derivative of these functions, you have to find the slope of the line at the point where x = 2

f'(2) = 2

g'(2) = 1

Then finally you plug that all into the equation we made at the beginning and get the answer

h'(2) = 4 x 1 + 5 x 2 = 14

So the answer is C

*If you are taking the AP exam on monday good luck! I am taking it too! :D