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# Absolute maxima and minima a. Find the | Ch 4.1 - 36E

ISBN: 9780321570567 2

## Solution for problem 36E Chapter 4.1

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition

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Problem 36E

Absolute maxima and minima a. Find the critical points of f on the given interval. b. Determine the absolute extreme values off on the given interval. c. Use a graphing utility to confirm your conclusions. f?? ?) = ?? ?3on [?8, 8]

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STEP_BY_STEP SOLUTION Step-1 Critical point definition ; Let f be a continuous function defined on an open interval containing a 1 number ācā.The number ācā is critical value ( or critical number ). If f (c) = 0 1 or f (c) is undefined. A critical point on that graph of f has the form (c,f(c)). Step-2 Absolute extreme values definition; 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 w ith domain D and let c b e a fixed constant in D . T en the output value f (c) 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_3 2/3 a). The given function is f(x) = (x) , on [-8,8].Clearly the function is polynomial function and it is continuous for all of x . Now , we have to find out the critical points of f on the given interval. Now , f(x) = (x) 2/3 then differentiate the function both sides with respect to x. f (x) = d (x)2/3 dx 2 (2/3)1 d n n1 = 3 (x) ,since dx ( x ) = nx . = 3 (x)1/3 Since , from the definition...

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