For the every value of x the function f(x) = 1 5^x is - Vidyadip

MCQ

For the every value of $ x$ the function $f(x) = {1 \over {{5^x}}}$ is

✓
Decreasing
B
Increasing
C
Neither increasing nor decreasing
D
Increasing for $x > 0 $ and decreasing for $x < 0$

✓

Answer

Correct option: A.

Decreasing

a
(a) $f(x) = {5^{ - x}}$

==>$f'(x) = - {5^{ - x}}{\log _e}5 = - \frac{{{{\log }_e}5}}{{{5^x}}}$

==> $f'(x) < 0$ for all $x$

$i.e.,$ $f(x)$ is decreasing for all $x.$

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

For $U_n = \int\limits_0^1 \, x^n (2 - x)^n\, dx$; $V_n = \int\limits_0^1 \, x^n (1 - x)^n \,dx\, n\, \in\, N$, which of the following statement $(s)$ is/are ture?

$\int_{}^{} {\frac{{x - 1}}{{{{(x + 1)}^3}}}{e^x}\;dx = } $

If $f(x) = \cos (\log x)$, then $f({x^2})f({y^2}) - \frac{1}{2}\left[ {f\,\left( {\frac{{{x^2}}}{2}} \right) + f\left( {\frac{{{x^2}}}{{{y^2}}}} \right)} \right]$ has the value

$\int_{}^{} {{e^{2x}}( - \sin x + 2\cos x)\;dx = } $

Choose the correct answer.Distance between the two planes$:\ 2x + 3y + 4z = 4$ and $4x + 6y + 8z = 12$ is:

$\int \frac{d x}{1-e^x}$ is equal to :

Four persons P, Q, R and S are initially at the four corners of a square side d. Each person now moves with a constant speed v in such a way that P always moves directly towards Q, Q towards R, R towards S, and S towards P. The four persons will meet after time.

The line $L$ given by $\frac{{x - 2}}{2} = \frac{{y - 1}}{b} = \frac{{z + 1}}{c}$ passes through the point $(1, 2, 3)$ . Another line $K$ is parallel to line $L$ and has the equation $\frac{{x + 2}}{a} = \frac{{y - 3}}{2} = \frac{{z + 4}}{d}$ . Then the distance between line $L$ and $K$ is

Let $a, b \in \mathbb{R}$ and $f: \mathbb{R} \rightarrow \mathbb{R}$ be defined by $f(x)=a \cos \left(\left|x^3-x\right|\right)+b|x| \sin \left(\left|t^3+x\right|\right)$. Then $f$ is

($A$) differentiable at $x=0$ if $a=0$ and $b=1$

($B$) differentiable at $x=1$ if $a=1$ and $b=0$

($C$) $NOT$ differentiable at $x=0$ if $a=1$ and $b=0$

($D$) $NOT$ differentiable at $x=1$ if $a=1$ and $b=1$

The equation $2\cos^{-1}\text{x}+\sin^{-1}\text{x}=\frac{11\pi}{6}$ has: