Question

Question #9d0c5

Answer 1

Choice e

Explanation:

The definition of the derivative is

`f'(x)=lim_(h->0)(f(x+h)-f(x))/h`

We are given `f(x)=3x^2-2sqrtx`

We also need to find `f(x+h)` which can be done by substituting `x+h` for `x` in the function

So...

`f(x+h)=3(x+h)^2-2sqrt(x+h)`

Given this we can rewrite the definition of the derivative and find the expression that will find `f'(x)`

Thus,

`f'(x)=lim_(h->0)((3(x+h)^2-2sqrt(x+h))-(3x^2-2sqrtx))/h`

So given the choices, this will be choice e