ecall that the Extreme Value Theorem guarantees that continuous functions have global axima and global minima over every closed, bounded interval. onsider the following mathematical statements. Fill in the blank with "all", "no", or "some" make the following statements true. Note that "some" means one or more instances, but t all. • If your answer is "all", then give a brief explanation as to why. • If your answer is "no", then give an example and a brief explanation as to why. • If your answer is "some", then give two specific examples that illustrate why your answer it not "all" or "no". Be sure to explain your two examples. real numbers b, if ƒ(x) = x², then ƒ has a global maximum on the interval a) For (0,b). ) For functions f, if f is differentiable and has a global minimum on the interval 0≤x≤6, then f'(x) = 0 for some x in the interval (0,6). c) For functions f, if f is continuous and differentiable on 0 ≤ x ≤ 7 and f has exactly one critical point at x = 4, then f has either a global maximum or minimum at x = 4.

ecall that the Extreme Value Theorem guarantees that continuous functions have global axima and global minima over every closed, bounded interval. onsider the following mathematical statements. Fill in the blank with "all", "no", or "some" make the following statements true. Note that "some" means one or more instances, but t all. • If your answer is "all", then give a brief explanation as to why. • If your answer is "no", then give an example and a brief explanation as to why. • If your answer is "some", then give two specific examples that illustrate why your answer it not "all" or "no". Be sure to explain your two examples. real numbers b, if ƒ(x) = x², then ƒ has a global maximum on the interval a) For (0,b). ) For functions f, if f is differentiable and has a global minimum on the interval 0≤x≤6, then f'(x) = 0 for some x in the interval (0,6). c) For functions f, if f is continuous and differentiable on 0 ≤ x ≤ 7 and f has exactly one critical point at x = 4, then f has either a global maximum or minimum at x = 4.

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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