Question

How do you find f'(x) using the definition of a derivative `f(x) = -3x^2 + 6`?

Answer 1

See explanation

Explanation:

The defintion of the derivative is

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

so we have that

#f'(x)=lim_(h->0)[-3(x+h)^2+6+3x^2-6]/h=> f'(x)=lim_(h->0)[-3h(h+2x)]/h=> f'(x)=lim_(h->0)-3(h+2x)=> f'(x)=-6x#