The abscissa(e) of the point(s), where the tangent to curve y=x3-3x2-9x+5 is parallel to the x -axis is(are)

Question

The abscissa(e) of the point(s), where the tangent to curve y=x3-3x2-9x+5 is parallel to the x -axis is(are) (A) x=0 (B) x=1 and -1 (C) x=1 and -3 (D) x= -1 and 3

Tardigrade Admin · Accepted Answer

y=x3-3x2-9x+5 ⇒ (d y/d x)=3x2-6x-9 We know that this equation gives the slope of the tangent to the curve. The tangent is parallel to x -axis. Therefore, 3x2-6x-9=0 ⇒ x=-1, 3 .

Q. The abscissa(e) of the point(s), where the tangent to curve $y = x^{3} - 3 x^{2} - 9 x + 5$ is parallel to the $x$ -axis is(are)

$x = 0$

$x = 1$ and $- 1$

$x = 1$ and $- 3$

$x = - 1 an d 3$

$y = x^{3} - 3 x^{2} - 9 x + 5$
$\Rightarrow$ $\frac{d y}{d x} = 3 x^{2} - 6 x - 9$
We know that this equation gives the slope of the tangent to the curve. The tangent is parallel to $x$ -axis.
Therefore, $3 x^{2} - 6 x - 9 = 0$
$\Rightarrow$ $x = - 1, 3$ .

Q. The abscissa(e) of the point(s), where the tangent to curve y=x3−3x2−9x+5 is parallel to the x -axis is(are)

x=0

x=1 and −1

x=1 and −3

x=−1and3