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 + 3x²- 2x³

✓

Answer

f(x) = 5 + 36x + 3x²- 2x³
$\therefore$ f'(x) = 36 + 6x - 6x²
Critical point
f'(x) = 0
⇒ 36 + 6x - 6x² = 0
⇒ -6(x² - x - 6) = 0
⇒ (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 "4 Marks" from Increasing and Decreasing Functions→Increasing and Decreasing Functions — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If y = (tan^–1x)², show that $\text{(x}^{2}+\text{1})^{2}\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}+\text{2x}(\text{x}^{2}+{1)}\frac{\text{dy}}{\text{dx}}=2.$

Find the general solution of the differential equation $\frac{d y}{d x}-y=\cos x$

Solve the following differential equation:
$(1+\text{x}^2)\frac{\text{dy}}{\text{dx}}-2\text{xy}=(\text{x}^2+2)(\text{x}^2+1)$

Integrate the function $\sqrt{1+3 x-x^{2}}$

An urn contains m white and n black balls. A ball is drawn at random and is put back into the urn along with k additional balls of the same colour as that of the ball drawn. A ball is again drawn at random. Show that the probability of drawing a white ball now does not depend on k.

Find all points of discontinuity of f, where
$\text{f(x)}=\begin{cases}\frac{\sin\text{x}}{\text{x}},\text{if x}<0\\ \text{x}+ 1, \text{if} \text{x}\geq0\end{cases}$

Let S be the set of all rational numbers except 1 and * be defined on S by a * b = a + b - ab, for all a, b ∈ S.
Prove that:

* is a binary operation on S.
* is commutative as well as associative.

Discuss the continuity of the following functions:

$\text{f(x)}=\sin\text{x}+\cos\text{x}$
$\text{f(x)}=\sin\text{x}-\cos\text{x}$
$\text{f(x)}=\sin\text{x}\cos\text{x}$

Evaluate the following integrals:
$\int\limits^{\text{a}}_{-\text{a}}\log\Big(\frac{\text{a}-\sin\theta}{\text{a}+\sin\theta}\Big)\text{d}\theta$

Find the angle between the lines whose direction cosines are given by the equations:
2l + 2m - n = 0, mn + ln + lm = 0