Download App

APPLICATION OF DERIVATIVES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAPPLICATION OF DERIVATIVES1 Mark
MCQ
Function $f(x) = x^3 - 27x + 5$ is monotonically increasing when:
  • A
    $\text{x}<-3$
  • ✓
    $|\text{x}|>3$
  • C
    $\text{x}\leq-3$
  • D
    $|\text{x}|\geq3$
✓

Answer

Correct option: B.
$|\text{x}|>3$
$f(x) = 3x^2 - 27x$
$\Rightarrow f'(x) = x^3 - 27x + 5$
$\Rightarrow f'(x) = 3(x^2 - 9)$
Function is increasing,
$3\big(\text{x}^2-9\big)\geq0$
$\Rightarrow\text{x}^2\geq9$
$\Rightarrow|\text{x}|\geq3$

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 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

Apply linear programming to this problem. A firm wants to determine how many units of each of two products (products D and E) they should produce to make the most money. The profit in the manufacture of a unit of product D is 100 and the profit in the manufacture of a unit of product E is100 and the profit in the manufacture of aunit of product E is 87. The firm is limited by its total available labor hours and total available machine hours. The total labor hours per week are 4,000. Product D takes 5 hours per unit of labor and product E takes 7 hours per unit. The total machine hours are 5,000 per week. Product D takes 9 hours per unit of machine time and product E takes 3 hours per unit. Which of the following is one of the constraints for this linear program?
→
$\int\cos^{-1}(\frac{1}{\text{x}})\text{dx}$ equals:
→
${d \over {dx}}({e^{{x^3}}})$ is equal to
→
If the straight lines $\vec r=$$(1,2,3)+k(\lambda ,2,3),k \in R$  and $\vec r=$$(2,3,1) +k(3,\lambda ,2),k \in R$ intersect at a point , then the interger $\;\lambda $ is equal to . 
→
Let a vector $\vec{a}$ be coplanar with vectors $\vec{b}=2 \hat{i}+\hat{j}+\hat{k}$ and $\vec{c}=\hat{i}-\hat{j}+\hat{k} .$ If $\vec{a}$ is perpendicular to $\vec{d}=3 \vec{i}+2 \hat{j}+6 \hat{k}$, and $|\vec{a}|=\sqrt{10} .$ Then a possible value of $[\overrightarrow{\mathrm{a}} \overrightarrow{\mathrm{b}} \overrightarrow{\mathrm{c}}]+[\overrightarrow{\mathrm{a}} \overrightarrow{\mathrm{b}} \vec{d}]+[\overrightarrow{\mathrm{a}} \vec{c} \vec{d}]$ is equal to:
→
The existance of the unique solution of the system of equations$2x + y + z = \beta $ , $10x - y + \alpha z = 10$ and $4x+ 3y-z =6$ depends on
→
$\int_{}^{} {\cos 2\theta \log \left( {\frac{{\cos \theta + \sin \theta }}{{\cos \theta - \sin \theta }}} \right)\;d\theta = } $
→
For positive integer $n$, define

$f(n)=n+\frac{16+5 n-3 n^2}{4 n+3 n^2}+\frac{32+n-3 n^2}{8 n+3 n^2}+\frac{48-3 n-3 n^2}{12 n+3 n^2}+\ldots+\frac{25 n-7 n^2}{7 n^2}$

Then, the value of $\lim _{ n \rightarrow \infty} f( n )$ is equal to

→
The differention equation $\frac{\text{dy}}{\text{dx}}+\text{P}\text{y}=\text{Qy}^{\text{n}},\text{n}>2$ can be reduced to linear from by substituting:
→
If $f(x) = {1 \over {\sqrt {{x^2} + {a^2}} + \sqrt {{x^2} + {b^2}} }}$, then $f'(x)$ is equal to
→