67. Proof of the Second Derivative Test Let c be a critical point such that f"(c) > 0 [the case f"(c) < 0 is similar]. (a) Show that f"(c) = lim (b) Use (a) to show that there exists an open interval (a, b) containing c such that f'(x) < 0 if a 0 if c < x < b. Conclude that f(c) is a local minimum. f'(c +h)

67. Proof of the Second Derivative Test Let c be a critical point such that f"(c) > 0 [the case f"(c) < 0 is similar]. (a) Show that f"(c) = lim (b) Use (a) to show that there exists an open interval (a, b) containing c such that f'(x) < 0 if a 0 if c < x < b. Conclude that f(c) is a local minimum. f'(c +h)

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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