Maximum and minimum

  1. 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
     
  2. jcsd
  3. HallsofIvy

    HallsofIvy 40,678
    Staff Emeritus
    Science Advisor

    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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