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Problem 3

$3-4$ . For each of the numbers $a, b, c, d, r,$ …

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Problem 2

Suppose $f$ is a continuous function defined on a closed
interval $[a, b] .$
(a) What theorem guarantees the existence of an absolute
maximum value and an absolute minimum value for $f ?$
(b) What steps would you take to find those maximum and
minimum values?

Answer

A.Extreme Value Theorem
B. Step $1 :$ Find all values of $x$ for which $f^{\prime}(x)=0$ or $f^{\prime}(x)$ is undefined.
Step $2 :$ Evaluate $f(x)$ at those values of $x$ as well as at the endpoints.
Step $3 :$ Compare these finitely many $f(x)$ to find the largest and smallest
value.



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