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Absolute maxima and minima a. Find the
Chapter 7, Problem 36E(choose chapter or problem)
31–42. 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
\(f(x)=x^{2 / 3}\) on [-8, 8]
Questions & Answers
QUESTION:
31–42. 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
\(f(x)=x^{2 / 3}\) on [-8, 8]
ANSWER:STEP_BY_STEP SOLUTION 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 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_