Absolute maxima and minima a. Find the critical points off

Chapter 7, Problem 48E

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QUESTION:

48–55. Absolute maxima and minima

a. Find the critical points of f on the given interval.

b. Determine the absolute extreme values of f on the given interval.

c. Use a graphing utility to confirm your conclusions.

\(f(x)=(x-2)^{1/2};\ \ [2,\ 6]\)

Questions & Answers

QUESTION:

48–55. Absolute maxima and minima

a. Find the critical points of f on the given interval.

b. Determine the absolute extreme values of f on the given interval.

c. Use a graphing utility to confirm your conclusions.

\(f(x)=(x-2)^{1/2};\ \ [2,\ 6]\)

ANSWER:

STEP_BY_STEP SOLUTION Step-1 Critical point definition ; Let f be a continuous function defined on an open interval containing a number ‘c’.The number ‘c’ is critical value ( or critical number ). If f (c) 1 1 = 0 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 afunction 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 i

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