Download App

Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives1 Mark
Question
Find the interval in function -2x3 - 9x2 - 12x + 1 is increasing or decreasing:
✓

Answer

It is given that function f(x) = -2x3 - 9x2 - 12x + 1
$\Rightarrow$ f '(x) = -6x2 - 18x + 12
$\Rightarrow$ f '(x) = -6(x2 + 3x + 6)
$\Rightarrow$ f '(x) = -6(x + 1)(x + 2)
If f '(x) = 0, then we get,
$\Rightarrow$ x = -1 and -2
So, the points x = -1 and x = -2 divides the real line into three disjoint intervals, $(-\infty,-2),(-2,-1)$ and $(-1, \infty)$ 
So, in intervals $(-\infty,-2),(-1, \infty)$
f '(x) = -6(x + 1)(x + 2) < 0
Therefore, the given function 'f ' is strictly decreasing for x < -2 and x > -1
Further, in interval (-2, -1)
f '(x) = -6(x + 1)(x + 2) > 0
Therefore, the given function (f) is strictly increasing for -2 < x < -1

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 "1 Marks" from Application of Derivatives→Application of Derivatives — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Prove that $\sin ^ { - 1 } \frac { 8 } { 17 } + \sin ^ { - 1 } \frac { 3 } { 5 } = \tan ^ { - 1 } \frac { 77 } { 36 }.$
→
Find the transpose of each of the following matrices:

$\begin{bmatrix}-1&5&6\\ \sqrt{3}&5&6\\2&3&-1\end{bmatrix}$

→
Given that the events A and B are such that P(A) = $\frac{1}{2}$, $P(A \cup B)=\frac{3}{5}$ and P(B) = p.
Find p if they are mutually exclusive.
→
If P(A) = $\frac{7}{13}$, P(B) = $\frac{9}{13}$ and $\mathrm{P}(\mathrm{A} \cap \mathrm{B})=\frac{4}{13}$, evaluate P(A|B).
→
Find the interval in function 6 - 9x - x2 is increasing or decreasing.
→
If A = $\left[\begin{array}{cc} {\cos \alpha} & {-\sin \alpha} \\ {\sin \alpha} & {\cos \alpha} \end{array}\right]$, and A + A' = I, if the value of $\alpha$ is
→
Find the integral: $\int \frac{x+2}{2 x^{2}+6 x+5} d x$
→
Find the principal value of ${\cos ^{ - 1}}\left( { - \frac{1}{2}} \right)$.
→
Show that f : N $ \to$ N, given by $ f ( x ) = \left\{ \begin{array} { l l } { x + 1 , } & { \text { if } x \text { is odd } } \\ { x - 1 , } & { \text { if } x \text { is even } } \end{array} \right.$is both one-one and onto.
→
Find local maximum and local minimum values of the function f given by f (x) = 3x4 + 4x3 – 12x2 + 12
→