Answer
$f(2)=2$
$f(2.1)=2.31525$
$f'(2)\approx 3.1525$
Work Step by Step
Evaluate $f(2)$ and $f(2.1)$. Then use the slope formula to estimate $f'(2)$:
$f(2)=\frac{1}{4}2^3$
$f(2)=2$
$f(2.1)=\frac{1}{4}2.1^3$
$f(2.1)=2.31525$
$f'(2)\approx \frac{2-2.32515}{2-2.1}$
$f'(2)\approx 3.1525$
