diff --git a/documents/math-minimal-distance-to-cubic-function/math-minimal-distance-to-cubic-function.tex b/documents/math-minimal-distance-to-cubic-function/math-minimal-distance-to-cubic-function.tex index 18688b2..cb6fc00 100644 --- a/documents/math-minimal-distance-to-cubic-function/math-minimal-distance-to-cubic-function.tex +++ b/documents/math-minimal-distance-to-cubic-function/math-minimal-distance-to-cubic-function.tex @@ -356,7 +356,7 @@ For all other points $P = (0, w)$, there are exactly two minima $x_{1,2} = \pm \ So the solution is given by \begin{align*} -x_S &:= - \frac{b}{2a}\\ +x_S &:= - \frac{b}{2a} \;\;\;\;\; \text{(the symmetry axis)}\\ \underset{x\in\mdr}{\arg \min d_{P,f}(x)} &= \begin{cases} x_1 = +\sqrt{a (y_p + \frac{b^2}{4a} - c) - \frac{1}{2}} + x_S \text{ and } &\text{if } x_P = x_S \text{ and } y_p + \frac{b^2}{4a} - c > \frac{1}{2a} \\ x_2 = -\sqrt{a (y_p + \frac{b^2}{4a} - c) - \frac{1}{2}} + x_S\\