Question

What does It mean when $\frac{dy}{dx}=0$?

Answer 1

Analysis of derivative of $\mathit{y}$ with respect to $\mathit{x}\mathbf{}$:

Meaning of $\frac{dy}{dx}=0$

1. $\frac{dy}{dx}$ denotes differentiating $y$with respect to $x.$
2. $\frac{dy}{dx}$ is the rate of change of $y$ with respect to the rate of change of $x$ in a very small interval.
3. When $\frac{dy}{dx}=0$, it means that the function is momentarily horizontal or the slope of the function at that instant is zero.

It is also the turning point, i.e., the point at which the function has a maximum or minimum value.

Hence the meaning of $\frac{dy}{dx}=0$ is explained.