Your classmate claims that the the function

f(x,y) = x^3(e^{x^2−3y^2})−(17−3x^2)(y−2)
does not have an absolute maximum nor an absolute minimum when the function is restricted to the disk x^2+y^2 ≤ 7.

Please explain why this is incorrect.

1 answer

the domain of exponentials is all reals.
The domain of all polynomials is all reals.

So, the domain of f(x,y) is all reals