CPM Homework Help : CALC Problem 3-45

Below is the graph of a function $f(x)$ with tangents drawn at $x = -2$ , $−1$ , $1$ , and $2$ . $f^{\prime}(0) = 0$ . Use the slopes provided in the graph to find the slope function $f^{\prime}(x)$ . Also, find $f(x)$ .

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.