Question

If h(2)=7 and h'(2)=-2,find d/dx [(h(x))/(x)] A. –11/4 B. 2 C. D. 8 E. 16

Answer 1

Answer:

A. $\frac{-11}{4}$

Remember that if f and g are functions with $g(x)\neq 0$ then, $\frac{d}{dx}\frac{f(x)}{g(x)}=\frac{f'(x)g(x)-g'(x)f(x)}{g(x)^2}$.

Then,

$\frac{d}{dx}\frac{h(x)}{x}=\frac{h'(x)x-h(x)}{x^2}$

Evaluating in x=2,

$\frac{h'(2)*2-h(2)}{2^2}=\frac{-4-7}{4}=\frac{-11}{4}$

Then the answer is A.