For all real values of x , increasing function f(x) is - Vidyadip

MCQ

For all real values of $x$ , increasing function $f(x)$ is

A
${x^{ - 1}}$
B
${x^2}$
✓
${x^3}$
D
${x^4}$

✓

Answer

Correct option: C.

${x^3}$

c
(c) Since $f(x) = {x^3} \Rightarrow f'(x) = 3{x^2},$

which is non-negative for all real values of $ x.$

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

$\int\frac{1}{7}\sin\Big(\frac{\text{x}}{7}+10\Big)\text{dx}$ is equal to :

If $f\left( {\frac{{3x - 4}}{{3x + 4}}} \right) = x + 2,\,x \ne -\frac{4}{3}$ , and $\int {f\left( x \right)dx = A\,\log \left| {1 - x} \right| + Bx + C} $ , then the ordered pair $(A,B) $ is equal to : (where $C$ is a constant of integration)

If $(0, 0),(a, 0)$ and $(0, b)$ are collinear, then:

If $f(x) = \left\{ \begin{array}{l}{x^2}\sin \frac{1}{x},\;\;\;{\rm{when\,\, }}x \ne 0\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,0,\,\,\,\,{\rm{when\,\,}}\,x = 0\end{array} \right.$, then

The lengths of the sides of a triangle are $10+ x ^{2}$, $10+ x ^{2}$ and $20-2 x ^{2}$. If for $x = k$, the area of the triangle is maximum, then $3 K ^{2}$ is equal to

If $A = \left[ {\begin{array}{*{20}{c}}{\cos \theta }&{ - \sin \theta }\\{\sin \theta }&{\cos \theta }\end{array}} \right]$, then which of the following statements is not correct

The area of the region bounded by the curve $x = 2y + 3$ and the lines $y = 1$ and $y = -1$ is:

What is the value of $ \sin-1(\sin 6)?$

If $\text{f(x)}=|\text{x}-\text{a}|\ \phi\ (\text{x}),$ where $\phi(\text{x})$ is continuous function, then:

Smaller area enclosed by the circle $x^2 + y^2 = 4$ and the line $x + y = 2$ is :