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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4.1 - Problem 3e
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4.1 - Problem 3e

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# What conditions must be met to ensure that a function has

ISBN: 9780321570567 2

## Solution for problem 3E Chapter 4.1

Calculus: Early Transcendentals | 1st Edition

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Problem 3E

What conditions must be met to ensure that a function has an absolute maximum value and an absolute minimum value on an interval?

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STEP_BY_STYEP SOLUTION Step_1 When an output value of a function is a maximum or a minimum over the entire domain of the function, the value is called the absolute maximum or the absolute minimum. Let f be a function with domain D and let c be a fixed constant in D. Then the output value f ) is the 1. Absolute maximum value of f on D if and only if f(x) f(c) , for all x in D. 2. Absolute minimum value of f on D if and only if f(c) f(x) , for all x in D. Step_2 Absolute extreme values _an examples; 2 1). The domain of f(x) = x is all real numbers and the range is all non-negative real numbers. The graph in the figure below suggests that the function has no absolute maximum value and has an absolute minimum of 0, which occurs at x = 0. Step_3 The Absolute extreme...

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