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Maximum and minimum

by minia2353
Tags: maximum, minimum
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minia2353
#1
May24-10, 12:40 AM
P: 13
1. The problem statement, all variables and given/known data

prove: if f(x) bigger or the same as 0 on an interval I and if f(x) has a maximum value on I at x0(0 is written small beside the x), then sqrt of f(x) also has a maxsimum value at x0. Similarily for minimum values. Hint: Use the fact that sqrt of x is an increasing function on the interval zero to plus infinity.

2. Relevant equations



3. The attempt at a solution
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HallsofIvy
#2
May24-10, 07:53 AM
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Looks pretty direct to me. If [itex]f(x_0)[/itex] is a maximum for f, then [itex]f(y)\le f(x_0)[/itex] for all y.Since square root is an increasing function, [itex]\sqrt{f(y)}\le \sqrt{f(x_0)}[/itex].


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