Prove that y=x² at x=0 has both a local and global minimum using first derivative test. I can prove it with a graph looking at it visually but how would you prove it with written words.

[tex] \frac{d}{dx} {x}^{2} = 2x \\ x = 0 \\ 2 \times 0 = 0[/tex]When the derivative equals zero, that point is either the maximum or minimum.[tex] {x}^{2} \geqslant 0[/tex]The smallest real value of x² is 0, which is at x = 0.Hence, x² at x = 0 has both a local and global minimum.