Question

The abscissae of the points, where the tangent to curve $y=x^3-3x^2-9x+5$ is parallel to $x$-axis are

• A. $x=0\&0$
• B. $x=1\&-1$
• C. $x=1\&-3$
• D. $x=-1\&3$

Answer 1

The correct option is D

$x=-1\&3$

Explanation For The Correct Option:

Finding abscissae of the points

The given curve is $y=x^3-3x^2-9x+5$

We know that coordinates of every point on the curve will be of the form $(x,y)$

And in $(x,y)$, $x$ is abscissa

Since tangents to the curve are parallel to x -axis

Therefore, slope of tangent will be zero.

Then, $\frac{dy}{dx}=0$.

$y=x^3-3x^2-9x+5$

Now differentiating the equation of curve with respect to $x$ and equating it to zero

$$\begin{gathered} \Rightarrow \frac{dy}{dx}=0 \\ \Rightarrow 3x^2–6x–9=0 \\ \Rightarrow x^2–2x–3=0 \\ \Rightarrow x^2–3x+x–3=0 \\ \Rightarrow x(x–3)+1(x–3)=0 \\ \Rightarrow (x+1)(x–3)=0 \\ \therefore x=-1\mathrm{or}3 \end{gathered}$$

Hence, option D is the correct answer.