Consider the function: $f(x)=4x^2+8x+10$

Recall that the definition of the derivative is:

$\underset{h0}{lim}\frac{f(x+h)-f(x)}{h}$

$($A$)$ In terms of $x$ and $h$ only, find a simplified expression for only the numerator of this expression, $f(x+h)-f(x)$ :

$f(x+h)-f(x)=$

$$

$($B$)$ Now find a simplified expression for the expression $\frac{f(x+h)-f(x)}{h}$ :

$\frac{f(x+h)-f(x)}{h}=$

$$

$($C$)$ So what is the derivative of $f(x)=4x^2+8x+10?$

$\underset{h0}{lim}\frac{f(x+h)-f(x)}{h}=$

$$