The abscissa of the points, where the tangent to the curve $y=x^3-3 x^2-9 x+5$ is parallel to $X$-axis are
The abscissa of the points, where the tangent to the curve $y=x^3-3 x^2-9 x+5$ is parallel to $X$-axis are
x=1 and -1
x=1 and -3
x=-1 and 3
x=0 and 1
Solution
We have $y=x^3-3 x^2-9 x+5$
$\therefore \frac{d y}{d x}=3 x^2-6 x-9$ and since tangent is parallel to $X$ axis, we write
$\begin{aligned}
& 3 x^2-6 x-9=0 \Rightarrow x^2-2 x-3=0 \text { i.e. }(x-3)(x+1)=0 \\
& \Rightarrow x=-1,3
\end{aligned}$