# maximum and minimum

by minia2353
Tags: maximum, minimum
 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
 Math Emeritus Sci Advisor Thanks PF Gold P: 38,879 Looks pretty direct to me. If $f(x_0)$ is a maximum for f, then $f(y)\le f(x_0)$ for all y.Since square root is an increasing function, $\sqrt{f(y)}\le \sqrt{f(x_0)}$.

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