### Home > CALC > Chapter 3 > Lesson 3.2.2 > Problem3-62

3-62.

Hanah wrote this derivative function: $f ^ { \prime } ( x ) = \lim\limits_ { h \rightarrow 0 } \frac { ( ( x + h ) ^ { 2 } - 3 ) - ( ( x - h ) ^ { 2 } - 3 ) } { 2 h }$

1. What is $f(x)$?

Hanah's (symmetrical difference) definition of the derivative; $f'(x)=\lim\limits_{h\rightarrow 0}\frac{f(x+h)-f(x-h)}{2h}$

$f(x) = x^2-3$
Find $f^{\prime}(x)$, which is also the value of the limit.

2. What is $f^{\prime}(x)$? (Note--Avoid the algebra by using the Power Rule.)

Power Rule
if $f(x) = x^n$
then $f^{\prime}(x) = nx^{n − 1}$
$f(x) = x^2 − 3$

$f^{\prime}(x) =$ __________

3. Use your slope function to find $f^{\prime}(0)$ and $f^{\prime}( 1 )$.

Evaluate.