Let $f(x) = x^2$

Graph $f$ on a graphing device, and use the graph to estimate the following 4 values

$f'(0) =$

$f'(\frac {1}{2}) =$

$f'(1) =$

$f'(2) =$

Use symmetry to deduce the following 3 values

$f'(-\frac {1}{2}) =$

$f'(-1) =$

$f'(-2) =$

Use the above results to guess a formula for $f'(x)$, then use the definition of derivative to prove that your guess is correct, enter the result below

$f'(x)=$