CPM Homework Banner

Home > CALC > Chapter 3 > Lesson 3.3.3 > Problem 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 and , 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.