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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4.1 - Problem 50e
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4.1 - Problem 50e

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# Absolute maxima and minima a. Find the | Ch 4.1 - 50E

ISBN: 9780321570567 2

## Solution for problem 50E Chapter 4.1

Calculus: Early Transcendentals | 1st Edition

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Problem 50E

Absolute maxima and minima a. Find the critical points off on the given interval. b. Determine the absolute extreme values off on the given interval. c. Use a graphing utility to confirm your conclusions. 2 ? f(x) = x 1/2( ?4) 0n [0,4] 5

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Solution 50E Step-1 Critical point definition ; Let f be a continuous function defined on an open interval containing a 1 number ‘c’.The number ‘c’ 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 be a fixed constant in D . Then 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 1/2 x2 a). The given function is f(x) = x (54) 0n [0,4] .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. 2 5/2 Now , f(x) = x 1/2 (54) = ( x5 4x 1/2) , for the critical points , we have to differentiate the function both sides with respect to x. d d x5/2 1/2 dx f (x) = dx ( 5 4x ) 1 d x5/2 d 1/2 d d f (x) = dx ( 5 ) (dx ),since dx ( u-v) = dx ( u) - dx = ( )( )( x (5/2)1) - 4 ( )x (1/2)) , since d ( x ) = nx 5 2 2 dx = 2 ( x ) - 2x 1/2) 1 1 3/2 1/2 Since , from...

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##### ISBN: 9780321570567

The answer to “Absolute maxima and minima a. Find the critical points off on the given interval. b. Determine the absolute extreme values off on the given interval. c. Use a graphing utility to confirm your conclusions. 2 ? f(x) = x 1/2( ?4) 0n [0,4] 5” is broken down into a number of easy to follow steps, and 44 words. Since the solution to 50E from 4.1 chapter was answered, more than 311 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. The full step-by-step solution to problem: 50E from chapter: 4.1 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This full solution covers the following key subjects: absolute, interval, given, graphing, determine. This expansive textbook survival guide covers 85 chapters, and 5218 solutions.

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