A continuous and differentiable function intersects thex-axis at points a and b, (a < b). The slope of the function at a is positive and the slope at b is negative. Which of the following is true for any such function? There exists some point on the interval (a, b) where (a) The slope is zero and the function has a local maximum. (b) The slope is zero but there is not a local maximum. (c) There is a local maximum but there does not have to be a point at which the slope is zero. (d) None of the above have to be true.

A continuous and differentiable function intersects thex-axis at points a and b, (a < b). The slope of the function at a is positive and the slope at b is negative. Which of the following is true for any such function? There exists some point on the interval (a, b) where (a) The slope is zero and the function has a local maximum. (b) The slope is zero but there is not a local maximum. (c) There is a local maximum but there does not have to be a point at which the slope is zero. (d) None of the above have to be true.

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 98E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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