Let $f(x)=2 x^2 + 4 x + 2$ and let $\displaystyle g(h)=\frac { f(3 +h)-f(3 ) }{ h }$.

Determine each of the following:

(a) $g(1) =$
(b) $g(0.1) =$
(c) $g(0.01) =$

You will notice that the values that you entered are getting closer and closer to a number $L$. This number is called the limit of $g(h)$ as $h$ approaches $0$ and is also called the derivative of $f(x)$ at the point when $x = 3$. We will see more of this when we get to the calculus textbook.

Enter the value of $L$: