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

1. Jul 23, 2011

### yungman

I want to check with you guys:

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

Thanks

Alan

2. Jul 23, 2011

### Spinnor

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?

3. Jul 23, 2011

### HallsofIvy

Staff Emeritus
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.