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

1 Answer
Oct 5, 2016

f'(x)=-6x

Explanation:

The derivative of a function f(x) is definited as:

Given f(x): RR->RR

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

Therefore, given:

f(x)=-3x^2+4

f'(x)=lim_(h->0)((-3(x+h)^2+4)-(-3x^2+4))/h=

=lim_(h->0)(-3(x^2+2hx+h^2)+4+3x^2-4)/h=

=lim_(h->0)(cancel(-3x^2)-6hx-3h^2cancel(+4)cancel(+3x^2)cancel(-4))/h=

=lim_(h->0)-3cancel(h)(2x+h)/cancel(h)=-6x