Prove the second case of Theorem 3.5. Data from in Theorem 3.6 THEOREM 3.5 Test for Increasing

Prove the second case of Theorem 3.5.

Data from in Theorem 3.6

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THEOREM 3.5 Test for Increasing and Decreasing Functions Let f be a function that is continuous on the closed interval [a, b] and differen- tiable on the open interval (a, b). 1. If f'(x) > 0 for all x in (a, b), then f is increasing on [a, b]. 2. If f'(x) < 0 for all x in (a, b), then fis decreasing on [a, b]. 3. If f'(x) = 0 for all x in (a, b), then fis constant on [a, b].