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# maximum/minimum values from graphs Use the following ISBN: 9780321570567 2

## Solution for problem 11E Chapter 4.1

Calculus: Early Transcendentals | 1st Edition

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Problem 11E

maximum/minimum values from graphs ?Use the? ?following graphs to identify the points? (?if any?) ?on the interval? [?a. b?] ?at which the function has cm absolute maximum value or an absolute minimum value.

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STEP_BY_STEP 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 c onstant 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. Example ; The Absolute extreme values on a restricted domain ; If th e domain of f(x ) = x is restricted to [-2, 3], the corresponding range is [0, 9]. As shown below, the graph on the interval[-2, 3] suggests that f has an absolute maximum of 9 at x = 3 and an absolute minimum of 0 at x = 0. Step-3 The given graph is; Now we need to verify the points , from the graph on the interval [a,b] at which the function has an absolute maximum value or absolute minimum value. From the graph it is clear that the given function y = h(x) is continuous on that given interval [a,b]. Since the graph has no holes or breaks in that interval. So, the function is continuous on [a,b]. We know the result that a function is continuous on the closed interval [a,b] has an absolute maximum value and an absolute minimum value on that interval . Hence , the graph y = h(x) is continuous on [a, b] . So , by the above results maximum value occurs at x= b , and the minimum value occurs at x= c 2 on [a, b].Since it is clearly mentioned in the graph. NOTE...

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##### ISBN: 9780321570567

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