AP CALCULUS:
The differentiable function g(x) has g(4) = 3 and g'(4) = -2.

Let f(x) = x • g(x). The equation of the line tangent to f at x = 4 is...

A) y = -8x + 35
B) y = 11x + 56
C) y = -2x + 20
D) y = -5x + 32

***I know the answer is D, but I don't know how to get there. I realize you use product rule, but because the numbers are given it's confusing. Please explain?

Question

AP CALCULUS:
The differentiable function g(x) has g(4) = 3 and g'(4) = -2.

Let f(x) = x • g(x). The equation of the line tangent to f at x = 4 is...

A) y = -8x + 35
B) y = 11x + 56
C) y = -2x + 20
D) y = -5x + 32

***I know the answer is D, but I don't know how to get there. I realize you use product rule, but because the numbers are given it's confusing. Please explain?

anonymous · Answer

$$f(x)=xg(x)$$
$$f'(x)=g(x)+xg'(x)$$ 
$$f'(4)=g(4)+4g'(4)$$ plug in the numbers, see what you get for the slope

anonymous · Answer

Thank you so much!