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

3-45.

Below is the graph of a function

*f*(*x*) with tangents drawn at*x*= −2, −1, 1, and 2.*f*′(0) = 0. Use the slopes provided in the graph to find the slope function*f*′(*x*). Also, find*f*(*x*). Homework Help ✎

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.