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If f is continous on ~[a,b~], then f attains an absolute maximum value f(c) and absolute minimum...

Question:

If f is continous on [a,b], then f attains an absolute maximum value f(c) and absolute minimum value f(d) at some numbers c and d in [a,b].

True

False

Maxima/Minima of a Function:

Given a function f(x), if it attains a maximum or minimum at a point a, then {eq}\frac{df}{dx} |_{x=a} =0 {/eq}

To know whether the point gives a maximum or a minimum, we can apply the second derivative test at that point. If the second derivative at that point is negative, then the point corresponds to a maximum. If the second derivative at the point is positive, then it corresponds to a minimum.

Answer and Explanation:

True. If f is continuous, then it has to achieve a maxima and minima in any given closed interval. If there is no explicit maxima and minima, the end points of the interval themselves will serve as maxima and minima points.


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Finding Minima & Maxima: Problems & Explanation

from General Studies Math: Help & Review

Chapter 5 / Lesson 2
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