Show that the maximum value of $x^2y^2z^2$ subject to the condition $x^2+y^2+z^2 = c^2$ is $\frac{c^6}{27}$. Interpret the result geometrically.
The above question is from Maxima and Minima concept of calculus. I am good with finding the maximum value.
But How to interpret geometrically. My approach is: The equation $x^2+y^2+z^2 = c^2$ represents a sphere with radius c.
I couldn't interpret the $x^2y^2z^2$. How it is related to above sphere.
please help me with the interpretation.