Question

How do you use the limit definition to find the derivative of `y=-3x^2+x+4`?

Answer 1

-6x+1

Explanation:

Using limit definition derivative of y, that is f(x) would be

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

= `Lim_(h->0) (-3(x+h)^2 +x+h +4 - (-3x^2 +x+4))/h`

=`Lim_(h->0) (-3x^2 -6xh -3h^2 +x+h+4 +3x^2 -x-4)/h`

= `Lim_(h->0) (-6xh-3h^2 +h)/h`

=`Lim_(h->0) -6x-3h+1`

=-6x+1