MCQ
For every value of $x $ function $f(x) = {e^x}$ is
  • A
    Decreasing
  • Increasing
  • C
    Neither increasing nor decreasing
  • D
    None of these

Answer

Correct option: B.
Increasing
b
(b) $f(x) = {e^x} \Rightarrow f'(x) = {e^x} > 0,\,\forall x$

Thus $f(x)$ is increasing 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

Similar questions

If $\int {f(x)\,\,dx = g(x),} $ then $\int {{f^{ - 1}}(x)} \,\,dx$ is equal to
The locus of xy + yz = 0 is:
  1. A pair of st. lines
  2. A pair of parallel lines
  3. A pair of parallel planes
  4. A pair of perpendicular planes
Let $f:[1, \infty) \rightarrow[2, \infty)$ be a differentiable function such that $f(1)=2$. If $6 \int_1^x f(t) d t=3 x f(x)-x^3$ for all $x \geq 1$, then the value of $f(2)$ is
The area common to the ellipse $\frac{\text{x}^2}{\text{a}^2}+\frac{\text{y}^2}{\text{b}^2}=1$ and $\frac{\text{x}^2}{\text{b}^2}+\frac{\text{y}^2}{\text{a}^2}=1,0<\text{b}<\text{a}$ is:
  1. $(\text{a}+\text{b})^2\tan^{-1}\frac{\text{b}}{\text{a}}$
  2. $(\text{a}+\text{b})^2\tan^{-1}\frac{\text{a}}{\text{b}}$
  3. $4\text{a}+\text{b}\tan^{-1}\frac{\text{b}}{\text{a}}$
  4. $4\text{a}+\text{b}\tan^{-1}\frac{\text{a}}{\text{b}}$
If $4\,P(A) = 6\,P\,(B) = 10\,P\,(A \cap B) = 1,$ then $P\,\left( {\frac{B}{A}} \right) = $
$\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{d x}{1+\sqrt{\tan x}}=$ __________  + C.
Let $R$ be an equivalence relation on a finite set $A$ having $n$ elements. Then the number of ordered pairs in $R$ is
The solution of $\frac{{dy}}{{dx}} + \frac{y}{3} = 1$ is
Let $a = i - j,\,\,b = j - k,\,\,c = k - i.$ If $\hat d$ is a unit vector such that $a\,.\,\hat d = 0 = [b\,\,c\,\,\hat d],$ then $\hat d$ is equal to
Let $A(2,3,5)$ and $C(-3,4,-2)$ be opposite vertices of a parallelogram $A B C D$ if the diagonal $\overrightarrow{B D}=\hat{i}+2 \hat{j}+3 \hat{k}$ then the area of the parallelogram is equal to