Question

At what points does the derivative of the function $y$ = $x^3$ coincide with the value of the function itself?

Answer 1

$y=x^3$

$\frac{dy}{dx}=3x^2$

Now, $y=\frac{dy}{dx}$

$⟹x^3=3x^2$

$⟹x^2(x-3)=0$

$⟹x=0,3$

Corresponding $y=0,27$

Hence. at points $(0,0)$ and $(3,27)$, value of function and its derivative are same.