### Home > CALC > Chapter 3 > Lesson 3.3.3 > Problem3-117

3-117.

Sketch a function $f(x)$ for which the following is true about its slope function $f^\prime(x)$.

• For $x < −3$, $f^\prime(x) > 0$ and the slope is increasing.

• For $−3 < x < −1$, $f^\prime(x) > 0$ and the slope is decreasing.

• At $x = −1$, $f^\prime(x)= 0$.

• For $x > −1$, $f^\prime(x) < 0$ and the derivative is decreasing.

Be careful! The clues give information about $f^\prime(x)$, but you are asked to sketch $f(x)$.

Translate: When $x$ is greater than $−3$, $f(x)$ is increasing and concave up.

Translate: When $x$ is in between $−3$ and $−1$, $f(x)$ is increasing and concave down.

Translate: When $x$ is exactly $−1$, $f(x)$ has reached a local maximum or minimum.

Translate: When $x$ is greater than $−1$, $f(x)$ is decreasing and concave down.

Remember that this graph is based on a slope statement. Without information about the exact $y$-values of $f(x)$,the entire sketch can be shifted vertically up or vertically down.