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

A.
`(-11)/(4)`

Remember that if f and g are functions with
`g(x)\\eq 0` then,
`(d)/(dx)(f(x))/(g(x))=(f'(x)g(x)-g'(x)f(x))/(g(x)^2)`.

Then,

`(d)/(dx)(h(x))/(x)=(h'(x)x-h(x))/(x^2)`

Evaluating in x=2,

`(h'(2)*2-h(2))/(2^2)=(-4-7)/(4)=(-11)/(4)`

Then the answer is A.