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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.

Continuous curve, coming from left above x axis, opening up, changing concavity, then turning at about (negative 1, comma 3), passing through the point (0, comma 2), continuing down & right, passing through the x axis between 0 & 1, label on left, x = negative 3, point of inflection, label by max, x = negative 1, local maximum.

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.