The function f(x) = 1 - e^ - x^2 /2 is - Vidyadip

MCQ

The function $f(x) = 1 - {e^{ - {x^2}/2}}$ is

A
Decreasing for all $ x$
B
Increasing for all $ x$
✓
Decreasing for $x < 0$ and increasing for $x > 0$
D
Increasing for $x < 0$ and decreasing for $x > 0$

✓

Answer

Correct option: C.

Decreasing for $x < 0$ and increasing for $x > 0$

c
(c) $f(x) = 1 - {e^{ - {x^2}/2}}$

$f'(x) = - {e^{ - {x^2}/2}}( - x) = x{e^{ - {x^2}/2}}$

For $f(x)$ to be increasing, $f'(x) > 0$

==> $x{e^{ - {x^2}/2}} > 0$

==> $x > 0$ and $f(x)$ to be decreasing for $x < 0$.

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

More "M.C.Q (1 Marks)" from 6. Application of derivatives→6. 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

The direction cosines of three lines passing through the origin are ${l_1},{m_1},{n_1};\,{l_2},{m_2},{n_2}$ and ${l_3},{m_3},{n_3}$. The lines will be coplanar, if

Correct evaluation of $\int_{}^{} {\frac{x}{{(x - 2)(x - 1)}}\;dx} $ is

(where $p$ is an arbitrary constant)

Let g(x) = 1 + x - [x] and $\text{f(x)}=\begin{cases}-1,&\text{x}<0\\0,&\text{x}=0\\1,&\text{x}>0\end{cases}$ where [x] denotes the greatest integer less than or equal to x. Then for all x, f(g(x)) is equal to:

x
1
f(x)
g(x)

Water is being filled at the rate of $1\, cm ^{3} / sec$ in a right circular conical vessel (vertex downwards) of height $35\, cm$ and diameter $14 \,cm$. When the height of the water level is $10\, cm$, the rate (in $cm ^{2} / sec$ ) at which the wet conical surface area of the vessel increases is

If the length of the perpendicular from the point $(\beta , 0, \beta )\, (\beta \neq 0)$ to the line $\frac{x}{1} = \frac{{y - 1}}{0} = \frac{{z + 1}}{{ - 1}}$ is $\sqrt {\frac{3}{2}} $, then $\beta $ is equal to

$\sin \left( {\frac{1}{2}{{\cos }^{ - 1}}\frac{4}{5}} \right) = $

$\int_{}^{} {\sqrt {\frac{{\cos x - {{\cos }^3}x}}{{1 - {{\cos }^3}x}}} \;dx} $ is equal to

The function f(x) = x − [x], where [⋅] denotes the greatest integer function is:

Continuous everywhere.
Continuous at integer points only.
Continuous at non-integer points only.
Differentiable everywhere.

The number of elements in the set $\left\{A=\left(\begin{array}{ll}a & b \\ 0 & d\end{array}\right): a, b, d \in\{-1,0,1\}\right.$ and $\left.(I-A)^{3}=I-A^{3}\right\}$ where $I$ is $2 \times 2$ identity matrix, is :

$\int\limits_{ - 1}^0 {\frac{{4{x^2} + 4x + 3}}{{1 + {e^{2x + 1}}}}} dx\, = $