### Home > CALC > Chapter 6 > Lesson 6.4.1 > Problem6-132

6-132.

For each graph below:

1. Trace $f(x)$ on your paper and write a slope statement for $f(x)$.

2. Sketch the graph of $f^\prime(x)$ using a different color.

Slope statements should tell a story, starting at the left side of the graph and ending at the right side.
There should be a description of where the function is increasing or decreasing and how the rate in which it is increasing or decreasing is changing.

Steep positive slopes on $f(x)$ should have very high $y$-values on the graph of $f^\prime(x)$. While steep negative slopes on $f(x)$ should have very low $y$-values on the graph of $f^\prime(x)$. Maxima and minima on $f(x)$ have $0$ slope, so they are roots on the graph of $f^\prime(x)$.