Find the intervals in which the following functions are increasin… - Vidyadip

Question

Find the intervals in which the following functions are increasing or decreasing. $f(x) = 5 + 36x + 3x^2- 2x^3$

✓

Answer

$f(x) = 5 + 36x + 3x^2- 2x^3$
$\therefore f'(x) = 36 + 6x - 6x^2$
Critical point
$f'(x) = 0$
$\Rightarrow 36 + 6x - 6x^2 = 0$
$\Rightarrow -6(x^2 - x - 6) = 0$
$\Rightarrow (x - 3)(x + 2) = 0$
$\therefore x = 3, -2$
Clearly $f'(x) > 0 $ if $-2 < x < 3$
Also $f'(x) < 0$ if $x < -2$ and $x > 3$
Thus increases if $\text{x}\in(-2,3),$ decreases if $\text{x}\in(-\infty,-2)\cup(3,\infty)$

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 "5 Marks Questions" from Increasing and Decreasing Functions→Increasing and Decreasing Functions — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Evaluate: $\int\limits_0^{\pi/2} 2 \sin x \cos x \tan^{-1 }(\sin x) dx.$

Draw the rough sketch of the curve $y=20 \cos 2 x ;\left(\right.$ where $\left.\frac{\pi}{6} \leq x \leq \frac{\pi}{3}\right)$
Using integration, find the area of the region bounded by the curve $y = 20 \cos2x$ from the ordinates
$x=\frac{\pi}{6}$ to $x=\frac{\pi}{3}$ and the $x-$axis.

In a game, a man wins ₹ 5 for getting a number greater than 4 and loses ₹ 1 otherwise, when a fair die is thrown. The man decided to throw a die three but to quit as and when he gets a number greater than 4. Find the expected value of the amount he wins/loses.

A pair of dice is thrown. Let E be the event that the sum is greater than or equal to 10 and F be the event "5 appears on the first-die". Find $\text{P}\Big(\frac{\text{E}}{\text{F}}\Big)$. If F is the event "5 appears on at least one die", find $\text{P}\Big(\frac{\text{E}}{\text{F}}\Big)$.

If $\text{y}=\text{e}^{\text{x}^2\cos\text{x}}+(\cos\text{x})^{\text{x}}, $ then find $\frac{\text{dy}}{\text{dx}}.$

At what points on the following curves, is the tangent parallel to $x-$axis? $y = 12(x + 1)(x - 2)$ on $[-1, 2]$

Examine the applicability of Mean Value Theorem for all three functions given in the above exercise 2.
$\text{f(x)}=[\text{x}]\text{ for x}\in[-2,\ 2]$

If $\text{y}=\sin(\sin\text{x})$ prove that $\frac{\text{d}^2\text{y}}{\text{dx}^2}+\tan\text{x}.\frac{\text{dy}}{\text{dx}}+\text{y}\cos^2\text{x}=0$

Maximum Z = 3x + 4y Subject to$\text{x}+\text{y}\leq30000$
$\text{y}\leq12000$
$\text{x}\geq6000$
$\text{x}\geq\text{y}$
$\text{x},\text{y}\geq0$

Find the minimum value of 3x + 5y subject to the constraints:
$-2\text{x}+\text{y}\leq4,\text{x}+\text{y}\geq3,$ $\text{x}-2\text{y}\leq2,\text{x},\text{y}\geq0.$