Consider the function $g(x) = 2^x$ , which is graphed below, along with the tangent lines to the graph at $x=-2,-1,0,1,2$.

(Click on graph to enlarge. You may have to resize the popup window.)

Use the provided grid to estimate the slope of each tangent line. Your estimates need to be within 10% of the correct answer.

$g'(-2) =$
$g'(-1) =$
$g'(0) =$
$g'(1) =$
$g'(2) =$

Recall that the derivative $g'(x)$ is also a function; you just computed five values of this function. On a piece of scratch paper, sketch a rough graph of $y=g'(x)$. Which of the following best describes the graph of the derivative $y=g'(x)$?