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Is the maximum of a function in 3 space a constant?

  1. Jul 23, 2011 #1
    I want to check with you guys:

    If [itex]\; A(R,\theta,\phi) \;[/itex] is a function of [itex] R,\theta,\phi\;[/itex] in 3 space. [itex]A_{max}\;[/itex] is the maximum value of A in a closed volume. Is [itex]A_{max}\;[/itex] a constant? Seem like it is a constant, but I want to verify.

    Thanks

    Alan
     
  2. jcsd
  3. Jul 23, 2011 #2

    Let the function be A = R*sin(theta)*cos(phi)

    The function is not constant but has maxima on the surface of a sphere of radius R.

    Does this help?
     
  4. Jul 23, 2011 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Yes, the maximum of a function in any space, is a single number and so is a constant.

    Note that this is not[]/b] a "local maximum" of which there may be many different values.
     
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