If f(x) = x^3 - 6 x^2 + 9x + 3 be a decreasing function, then x l… - Vidyadip

MCQ

If $f(x) = {x^3} - 6{x^2} + 9x + 3$ be a decreasing function, then $x $ lies in

A
$( - \infty , - 1) \cap (3,\,\infty )$
✓
$(1,\,\,3)$
C
$(3,\,\,\infty )$
D
None of these

✓

Answer

Correct option: B.

$(1,\,\,3)$

b
(b) $f(x) = {x^3} - 6{x^2} + 9x + 3$,

For decreasing $f'(x) < 0$

==> $3{x^2} - 12x + 9 < 0$

==> ${x^2} - 4x + 3 < 0$

==> $(x - 3)\,\,(x - 1) < 0$,

$\therefore$ $x \in (1,\,3)$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 12 - 6. Application of derivatives→STD 12 - 6. Application of derivatives — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

The taxi fare in a city is as follows. For the first km the fare is Rs.10 and subsequent distance is Rs.6/ km.Taking the distance covered as x km and fare as Rs y, write a linear equation.

The probability that in a year of $22^{nd}$ century chosen at random, there will be $53$ Sunday, is

If $S$ is the sum of the first $10$ terms of the series $\tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{7}\right)+\tan ^{-1}\left(\frac{1}{13}\right)+\tan ^{-1}\left(\frac{1}{21}\right)+\ldots$ then $\tan ( S )$ is equal to

If the length of the perpendicular drawn from the point $P ( a , 4,2), a >0$ on the line $\frac{x+1}{2}=\frac{y-3}{3}=\frac{z-1}{-1}$ is $2 \sqrt{6}$ units and $Q \left(\alpha_{1}, \alpha_{2}, \alpha_{3}\right)$ is the image of the point $P$ in this line, then $a+\sum_{i=1}^{3} \alpha_{i}$ is equal to.

Let $\vec{a}=\hat{i}-\hat{j}+2 \hat{k}$ and $\vec{b}$ be a vector such that $\vec{a} \times \vec{b}=2 \hat{i}-\hat{k}$ and $\vec{a} \cdot \vec{b}=3$. Then the projection of $\vec{b}$ on the vector $\vec{a}-\vec{b}$ is :-

The function $f(x)=\left\{\begin{array}{cc}x^2 & \text { for } x<1 \\ 2-x & \text { for } x \geq 1\end{array}\right.$ is

Let $S$ be the set of values of $\lambda$, for which the system of equations

$6 \lambda x-3 y+3 z=4 \lambda^2$

$2 x+6 \lambda y+4 z=1$

$3 x+2 y+3 \lambda z=\lambda \text { has no solution. Then } 12 \sum_{\lambda \in S}|\lambda|$ is equal to $...........$.

Cosine of the angle between two diagonals of acube is equal to:

The maximum area (in sq. units) of a rectangle having its base on the $x-$ axis and its other two vertices on the parabola, $y = 12 -x^2$ such that the rectangle lies inside the parabola, is

Which of the following differentials equation has $y = x$ as one of its particular solution?