Finding a function with constrained second partials
Chapter , Problem 4AAE(choose chapter or problem)
Finding a function with constrained second partials Suppose that f is a twice-differentiable function of r, that that f is a twice-cion
\(r=\sqrt{x^{2}+y^{2}+z^{2}}\), and that
\(f_{x x}+f_{y y}+f_{z z}=0\)
Show that for some constants a and b,
\(f(r)=\frac{\underline{a}}{r}+b\)
Equation Transcription:
Text Transcription:
r=sqrt x^2 +y^2 +z^2
f_xx + f_yy + f_zz =0
f(r)=a/r + b
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