### Home > CALC > Chapter 3 > Lesson 3.2.1 > Problem3-45

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 $f(x)$.

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

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).

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