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3-117.

Sketch a function for which the following statements are 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.