Question

Suppose f(x) and g(x) are functions of x differentiable at x = 4. Given that f(4) = 3, f'(4) = -2, g(4) = 6, g'(4) = -4, find the value of each of the following.

a. Derivative of f(x) * g(x)

My answer: -27

b. Derivative of (f(x))/(g(x))

My answer: 1/12

c. Derivative of (g(x))/(f(x))

My answer: -1/3

d. A tangent line to f(x) at x = 4.

My answer: -2x + 11 (not sure)

Answer 1

a) let y = f(x) * g(x)
then y' = f(x)* g '(x) + g(x) * f '(x)
given:
f(4) = 3
f '(4) = -2
g(4) = 6
g '(4) = -4
so
y' = 3(-4) + 6(-2) = -24

how did you get -27 ?

do the others the same way

Answer 2

I'm sorry, g'(x) = -5.