I need to find the global maximum and minimum of the function $f(x,y)=2x^3-3x^2+y^2-2y$. For the critical points, I get $\nabla f(x,y)=(6x^2-6x,2y-2)$. Which results in $x=0, 1, y=1$. Next, I want to find the global maximum and minimum. Since this there is no interval of restriction on this function, I need to find the highest and lowest point of this 3D function, how do I go about doing that?
Find the global maximum and minimum of this function
calculusfunctions
Best Answer
Since $$\lim_{x\to\infty}f(x,0)=\lim_{x\to\infty}\left(2x^3-3x^2\right)=\infty$$ and $$\lim_{x\to-\infty}f(x,0)=\lim_{x\to-\infty}\left(2x^3-3x^2\right)=-\infty$$ this function doesn't have global extrema. Are you sure that there isn't a restriction on the domain of $f$?