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

3-117.

Sketch a function for which the following is true about its slope function

.

For

,and the slope is increasing.For

, and the slope is decreasing.At

,.For

,and the derivative is decreasing.

Be careful! The clues give information about , but you are asked to sketch

*.*

Translate: When is greater than

*is increasing and concave up.*

Translate: When is in between

*is increasing and concave down.*

Translate: When is exactly

*has reached a local maximum or minimum.*

Translate: When is greater than

*is decreasing and concave down.*

Remember that this graph is based on a slope statement. Without information about the exact -values of

*,the entire sketch can be shifted vertically up or vertically down.*