Difference between maximum and minimum values of f(x) = x^4e^ -x^… - Vidyadip

MCQ

Difference between maximum and minimum values of $f(x) = x^4e^{-x^2} \ \ \forall x \in R,$ is -

A
$\frac{4}{e^2} - \frac{2}{e}$
B
$\frac{4}{e} - \frac{2}{e^2}$
✓
$\frac{4}{e^2}$
D
$\frac{2}{e}$

✓

Answer

Correct option: C.

$\frac{4}{e^2}$

c
$f^{\prime}(x)=0$ at $x=0, \pm \sqrt{2}$

$f(\mathrm{x})_{\max }=\frac{4}{\mathrm{e}^{2}} ; f(\mathrm{x})_{\min }=0$

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

$50 \tan \left(3 \tan ^{-1}\left(\frac{1}{2}\right)+2 \cos ^{-1}\left(\frac{1}{\sqrt{5}}\right)\right)+4 \sqrt{2} \tan \left(\frac{1}{2} \tan ^{-1}(2 \sqrt{2})\right)$ is equal to

The sum of focal distances of any point on the ellipse with major and minor axes as $2a$ and $2b$ respectively, is equal to

${\log _4}18$ is

Two tangents are drawn from a point $P$ on radical axis to the two circles touching at $Q$ and $R$ respectively then triangle formed by joining $PQR$ is

$\int\limits_0^{\frac{\pi }{2}} { {\frac{{4x\sin \,x\, + \,{x^2}\,\cos \,x}}{{2\sqrt {\sin \,x} }}} dx }$ is equal to

The locus of the points $z$ which satisfy the condition arg $\left( {\frac{{z - 1}}{{z + 1}}} \right)$ =$\frac{\pi }{3}$ is

If $\int {{e^{{x^2}}}\left( {2 - \frac{1}{{{x^2}}}} \right)dx = {e^{{x^2}}}f(x) + C} $ and $f\left( {\frac{1}{2}} \right) = 2$ , then $f(1)$ is equal to (where $C$ is an arbitrary constant)

Solution of differential equation $x\,dy - y\,dx = 0$ represents

Let $\vec{a}$ and $\vec{b}$ be the vectors along the diagonal of a parallelogram having area $2 \sqrt{2}$. Let the angle between $\vec{a}$ and $\vec{b}$ be acute. $|\vec{a}|=1$ and $|\vec{a} . \vec{b}|=|\vec{a} \times \vec{b}| .$ If $\vec{c}=2 \sqrt{2}(\vec{a} \times \vec{b})-2 \vec{b}$, then an angle between $\vec{b}$ and $\vec{c}$ is

Let $\cos ^{-1}(x) + \cos ^{-1} (2x) + \cos ^{-1}(3x) = \pi.$ If $x$ satisfies the cubic $ax^3 + bx^2 + cx -1 = 0,$ then $(a + b + c)$ has the value equal to -