CPM Homework Help : APCALC Problem 3-45

At right is the graph of a function $f$ with tangent lines drawn at $x = −2, −1, 1,$ and $2$ . $f ^\prime(0) = 0$ . Use the slopes provided in the graph to write the slope function $f^\prime$ . Also, write an equation for $f$ .

Step 1:

First make a prediction about the shape of the slope graph. The original graph is a parabola. What will the slope graph look like?

Step 2:

Next, make a table showing $x$ -values and their corresponding slopes. Be sure to include that when $x = 0$ , the slope is $0$ (after all, look at the horizontal tangent line).

Step 3:

Use your table to find an equation of the slope function.

Upward parabola, vertex at the origin, with 4 highlighted points, each with line tangent to the curve at the point, & labeled as follows: at x = negative 2, label is m = negative 8, at x = negative 1, label is, m = negative 4, at x = 1, label is m = 4, at x = 2, label is m = 8.