If the tangent line at a point

Question:

If the tangent line at a point $(x, y)$ on the curve $y=f(x)$ is parallel to $x$-axis, then write the value of $\frac{d y}{d x}$.

Solution:

Given curve $y=f(x)$ has a point $(x, y)$ which is parallel to $x$-axis.

We know that the slope of the $x$-axis is $0 .$

$\because$ the point lies on the given curve

$\therefore$ Slope of the tangent $\frac{d y}{d x}=0$

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