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

1. What is the equation of $f(x)$?

   Hint 1(a):

   Hanah's (symmetrical difference) definition of the derivative;

   $f^\prime(x)=\lim\limits_{h\rightarrow 0}\frac{f(x+h)-f(x-h)}{2h}$

   Hint 2(a):

   $f(x) = x^2 − 3$

   Find $f^\prime (x)$, which is also the value of the limit.

2. What is the equation of $f^\prime (x)$? (Note: Avoid the algebra by using the Power Rule.)

   Hint (b):

   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 calculate $f^\prime(0)$ and $f^\prime (1)$.

   Hint (c):

   Evaluate.