If anyone could help with the intuition for solving and going about the following relative extrema problem, it would be greatly appreciated. The problem is as follows:
Determine point(s) on $y = x^2 + 1$ that are closest to the point $(0,2)$.
Thank you!
Considering the function $$f(x)=\sqrt{x^2+(x^2-1)^2}$$ we have to find the minimum: $$h(x)=x^2+(x^2-1)^2$$ $$h'(x)=2x+2(x^2-1)2x$$ $$h'(x)=2x(2x^2-1)$$ Can you finish?