Download App

Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives1 Mark
MCQ
The function $f(x)=1-x^3-x^5$ is decreasing for
  • A
    $1 \leq x \leq 5$
  • B
    $x \leq 1$
  • C
    $x \geq 1$
  • ✓
    all values of $x$
✓

Answer

Correct option: D.
all values of $x$
(d) : Given, $f(x)=1-x^3-x^5$
Differentiating w.r.t. $x$, we get
$
f^{\prime}(x)=-3 x^2-5 x^4
$
$\Rightarrow f^{\prime}(x)=-\left(3 x^2+5 x^4\right) \Rightarrow f^{\prime}(x)<0$ for all 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 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

Find the value of $x, \,y$ and $z$ from the following equation : $\left[\begin{array}{ll}4 & 3 \\ x & 5\end{array}\right]=\left[\begin{array}{ll}y & z \\ 1 & 5\end{array}\right]$
→
Choose the correct answer from the given four options : let $\text{P}(\text{A})=\frac{7}{13},\text{P}(\text{B})=\frac{9}{13}$ and $\text{P}(\text{A}\cup\text{B})=\frac{4}{13}.$ Then $\text{P}\Big(\frac{\text{A'}}{\text{B}}\Big)$ is equal to :
→
If $\sin^{-1}\Big(\frac{2\text{a}}{1-\text{a}^2}\Big)+\cos^{-1}\Big(\frac{1-\text{a}^2}{1+\text{a}^2}\Big)=\tan^{-1}\Big(\frac{2\text{x}}{1-\text{x}^2}\Big),$ where $\text{a},\text{x}\in(0,1),$ then the value of x is:
→
$\int_0^{\pi /2} {{{\sin }^{2m}}x\,dx = } $
→
The value of aa for which the area between the curves $y^2=4 a x$ and $x^2=4 a y$ is $1\ sq$. unit, is:
→
Choose the correct answer from the given four option.The degree of the differential equation $\Big[1+\Big(\frac{\text{d}\text{y}}{\text{d}\text{x}}\Big)^2\Big]^{\frac{3}{2}}=\frac{\text{d}^2\text{y}}{\text{d}\text{x}^2}$ is:
→
If $\frac{{dy}}{{dx}} = y + 3 > 0\;,\;y\left( 0 \right) = 2$, then $y\left( {\ln 2} \right)$ is equal to :
→
Considering only the principal values of the inverse trigonometric functions, the value of

$\frac{3}{2} \cos ^{-1} \sqrt{\frac{2}{2+\pi^2}}+\frac{1}{4} \sin ^{-1} \frac{2 \sqrt{2} \pi}{2+\pi^2}+\tan ^{-1} \frac{\sqrt{2}}{\pi}$ is. . . . 

→
Consider $f(x) =$ $\left[ {\frac{{2\,\,\left( {\sin \,x\,\, - \,\,{{\sin }^3}\,x} \right)\,\, + \,\,\left| {\sin \,x\,\, - \,\,{{\sin }^3}\,x} \right|}}{{2\,\,\left( {\sin \,x\,\, - \,\,{{\sin }^3}\,x} \right)\,\, - \,\,\left| {\sin \,x\,\, - \,\,{{\sin }^3}\,x} \right|}}} \right]$ , $x \ne \,\frac{\pi}{2} \,for\, x \in (0, \pi ) f(\pi /2) = 3$

where [ ] denotes the greatest integer function then,

→
The value of $\sin(2\tan^{-1}(0.75))$ is equal to:
→