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3-164.
  1. Draw the graph of f(x) given the following information about its slope function, f(x). Homework Help ✎

    • f ′(x) > 0 on 1 < x < 4

    • f ′(x) < 0 on x < 1 and x > 4

    • f ′(x) = 0 for x = 1, x = 4

Notice that the clues describe f '(x), yet you are asked to sketch f(x).

f '(x) > 0 on 1 < x < 4
Translate: f(x) is increasing between x = 1 and x = 4.

f '(x) < 0 on x < 1 and x > 4
Translate: f(x) is decreasing before x = 1 and after x = 4.

f '(x) = 0 for x = 1, x = 4
Translate: x has reached a local maximum or local minimum at x = 1 and x = 4.