Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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![7.
Assume that f is continuous and differentiable on (-xx, o0). Consider the interval (a, b) where a <b
are real numbers. Which of the following statement(s) is/are TRUE?
If you believe it is true, justify your reasoning. If you believe it is false, show it with an example.
(a) There is a number e in the interval (a, b] such that f(c) is the absolute minimum of f on [a, b).
(b) There is a number e in the interval (a, b) such that f (c) = 0.
(c) If f(b) <7< f(a). then there exists a number e in the interval (a, b) such that f(e) = 7.
7
(d) If f(a) = 7 and f(b) = 0, then there exists a number e in the interval (a, b) such that f'(c)
a.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc9f56476-a681-4415-ba15-86fa0a2c1533%2F31cc23a9-35b0-437c-addd-e4096f938baa%2Fk0o6rt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:7.
Assume that f is continuous and differentiable on (-xx, o0). Consider the interval (a, b) where a <b
are real numbers. Which of the following statement(s) is/are TRUE?
If you believe it is true, justify your reasoning. If you believe it is false, show it with an example.
(a) There is a number e in the interval (a, b] such that f(c) is the absolute minimum of f on [a, b).
(b) There is a number e in the interval (a, b) such that f (c) = 0.
(c) If f(b) <7< f(a). then there exists a number e in the interval (a, b) such that f(e) = 7.
7
(d) If f(a) = 7 and f(b) = 0, then there exists a number e in the interval (a, b) such that f'(c)
a.
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