This is an exercise that was given to me.
A particle starts at (0,0) and moves along parabola $y=\dfrac{1}{4}x^2$, $x\geq 0$. In which point of the curve the rate of change of $x$ is equal the rate of change of $y$? Suppose $x'(t)>0$ for all $t\geq0$.
Μy question is related to the assumptions of the exercise. It is necessary the assumption $x'(t)>0$ for all $t\geq0$?