How do you find f'(2) using the limit definition given $f(x)= 9-x^2$ ?

Question

17420 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-09T16:47:28

-4

enter image source here

Answer 2 · 2017-01-09T16:50:31

-4

Using the limit definition, you get:

$f'(2)=lim_(x->2)(f(x)-f(2))/(x-2)$

$=lim_(x->2)((9-x^2)-(9-2^2))/(x-2)$

$=lim_(x->2)(9-x^2-5)/(x-2)$

$=lim_(x->2)(4-x^2)/(x-2)$

$=lim_(x->2)-(x^2-4)/(x-2)$

$=lim_(x->2)-(cancel((x-2))(x+2))/cancel(x-2)$

$=-(2+2)=-4$

How do you find f'(2) using the limit definition given f(x)= 9-x^2f(x)= 9-x^2?