Question

If f and g are differentiable functions for all real values of x such that f(2) = 5, g(2) = 3, f '(2) = 1, g '(2) = -2, then find h '(2) if h(x) = f(x) g(x).

Answer 1

`h'(2)=-7`

Explanation:

So we have:

`h(x)=f(x)g(x)`

Differentiate. Use the product rule:

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

Substitute 2 for x:

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

We know that f'(2) is 1, f(2) is 5, g(2) is 3, and g'(2) is -2. Make the appropriate substitutions:

`h'(2)=(1)(3)+(5)(-2)`

Simplify:

`h'(2)=3-10`

Subtract:

`h'(2)=-7`