In which interval is the given function f(x) = 2 x^3 - 15 x^2 + 3… - Vidyadip

MCQ

In which interval is the given function $f(x) = 2{x^3} - 15{x^2} + 36x + 1$ is monotonically decreasing

A
$[2, 3]$
✓
$(2, 3)$
C
$( - \infty ,\,2)$
D
$(3,\,\infty )$

✓

Answer

Correct option: B.

$(2, 3)$

b
(b) $y = f(x) = 2{x^3} - 15{x^2} + 36x + 1$

$\frac{{dy}}{{dx}} = f'(x) = 6{x^2} - 30x + 36 = 6({x^2} - 5x + 6)$

$f'(x) = 6(x - 2)(x - 3)$

To be monotonic decreasing, $f'(x) < 0$

$ \Rightarrow (x - 2)(x - 3) < 0 \Rightarrow x \in (2,3)$.

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

$\cot ^{-1} \frac{\sqrt{1-x^2}}{x}$ equal to :

$\int_0^1 {\log \sin \left( {\frac{\pi }{2}x} \right)} \,dx = $

The value of $\int \frac{\sec x}{\operatorname{cosec}^2 x} d x$

Choose the correct answer from the given four options.
In a college, 30% students fail in physics, 25% fail in mathematics and 10% fail in both. One student is chosen at random. The probability that she fails in physics if she has failed in mathematics is:

The roots of the equation $\left| {\,\begin{array}{*{20}{c}}x&0&8\\4&1&3\\2&0&x\end{array}\,} \right| = 0$ are equal to

The corner points of the feasible region are $A(3,3), B(20,3), C(20,10), D(18,12)$ and $E(12, 12)$. The maximum value of $Z=2 x+3 y$ is $.......$

A fair coin is tossed $99$ times. If $X$ is the number of times head appears, then $P(X = r)$ is maximum when $r$ is:

If the curve a $y + x^2 = 7$ and $x^3 = y$, cut orthogonally at $(1, 1)$ then the value of a is:

Choose the correct answer from the given four options.If $\text{P}(\text{A})=\frac{2}{5},\text{P}(\text{B})=\frac{3}{5}$ and $\text{P}(\text{A}\cap\text{B})=\frac{1}{5},$ then $\text{P}\Big(\frac{\text{A}'}{\text{B}'}\Big)\cdot\text{P}\Big(\frac{\text{B}'}{\text{A}'}\Big)$ is equas :

Choose the correct answer from the given four options.The general solution of the differential equation $(\text{e}^{\text{x}}+1)\text{ydy}=(\text{y}+1)\text{e}^{\text{x}}$ is :