There exists a differentiable function f (-1, 1)→ R that does not have any local extrema but whose derivative vanishes at one point in (-1, 1). Select one: Ⓒa. True, here is an example: f(x) = x³. O b. True, because f is continuous on (-1, 1) which is an interval and thus it has a maximum and a minimum on that interval, and its derivative vanishes at these points by the IET. O c. False, because by the IET if f'(c) = 0 with c E (-1, 1) then c is at least a local extremum of f. O d. True, here is an example: f(x) = sin(x).

There exists a differentiable function f (-1, 1)→ R that does not have any local extrema but whose derivative vanishes at one point in (-1, 1). Select one: Ⓒa. True, here is an example: f(x) = x³. O b. True, because f is continuous on (-1, 1) which is an interval and thus it has a maximum and a minimum on that interval, and its derivative vanishes at these points by the IET. O c. False, because by the IET if f'(c) = 0 with c E (-1, 1) then c is at least a local extremum of f. O d. True, here is an example: f(x) = sin(x).

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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