Question

If f and g are differentiable functions for all real values of x such that f(1) = 4, g(1) = 3, f '(3) = −5, f '(1) = −4, g '(1) = −3, g '(3) = 2, then find h '(1) if h(x)= f(x)/g(x)

Answer 1

what is h'(x) ? apply quotient rule.

Answer 2

I got -3.

Answer 3

nope, show your work, please

Answer 4

I did f'(1)=-4 times g(1)= 3 + f(1)=4 times g'(1) =-3 and got -3 and I got -24 my bad.

Answer 5

The quotient rule says:
\(h'(x) =\dfrac{f'(x) g(x) -g'(x)f(x)}{g^2(x)}\)
\(h'(1) =\dfrac{f'(1) g(1) -g'(1)f(1)}{g^2(1)}=\dfrac{(-4)*3-((-3)*4)}{3^2}=\dfrac{-12+12}{9}=\dfrac{0}{9}=0\)

Answer 6

Okay thank you!