Download App

STD 12 - 6. Application of derivatives — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 6. Application of derivatives4 Marks
MCQ
Given function $f(x) = \left( {{{{e^{2x}} - 1} \over {{e^{2x}} + 1}}} \right)$ is
  • ✓
    Increasing
  • B
    Decreasing
  • C
    Even
  • D
    None of these
✓

Answer

Correct option: A.
Increasing
a
(a) $f(x) = \frac{{{e^{2x}} - 1}}{{{e^{2x}} + 1}}$

==>$f( - x) = \frac{{{e^{ - 2x}} - 1}}{{{e^{ - 2x}} + 1}} = \frac{{1 - {e^{2x}}}}{{1 + {e^{2x}}}}$==>$f(x) = - \frac{{{e^{2x}} - 1}}{{{e^{2x}} + 1}} = - f(x)$

==> $f(x)$ is an odd function.

Again $f(x) = \frac{{{e^{2x}} - 1}}{{{e^{2x}} + 1}} \Rightarrow f'(x) = \frac{{4{e^{2x}}}}{{{{(1 + {e^{2x}})}^2}}} > 0\,\forall \,n \in R$

==> $f(x)$ is an increasing function.

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

If $\cos 7\theta = \cos \theta - \sin 4\theta $, then the general value of $\theta $ is
→
Let $\alpha, \beta$ be the roots of the equation $x^2-x+2=0$ with $\operatorname{Im}(\alpha)>\operatorname{Im}(\beta)$. Then $\alpha^6+\alpha^4+\beta^4-5 \alpha^2$ is equal to
→
If the straight lines $\frac{x-1}{2}=\frac{y+1}{k}=\frac{z}{2}$ and $\frac{x+1}{5}=\frac{y+1}{2}=\frac{z}{k}$ are coplanar, then the plane$(s)$ containing these two lines is(are)

$(A)$ $y+2 z=-1$ $(B)$ $y+z=-1$ $(C)$ $y-z=-1$ $(D)$ $y-2 z=-1$

→
The foci of the ellipse $25{(x + 1)^2} + 9{(y + 2)^2} = 225$ are at
→
Let $f$ be a differentiable function such that $x ^2 f ( x )- x =4 \int \limits_0^x t f(t) d t, f(1)=\frac{2}{3}$.Then $18 f(3)$ is equal to $......$.
→
If the equation $x^8 - kx^2 + 3 = 0$ has a real solution, then least integral value of $k$ is-
→
The matrix $A = \frac{1}{3}\left[ {\begin{array}{*{20}{c}}1&2&2\\2&1&{ - 2}\\{ - 2}&2&{ - 1}\end{array}} \right]$is
→
If  $ a$  and $b$ are unit vectors such that $a \times b$ is also a unit vector, then the angle between $a$  and $ b$ is
→
Let $I_n=\int_0^{\pi / 2} x^n \cos x d x$, where $n$ is a non-negative integer. Then, $\sum \limits_{n=2}^{\infty}\left(\frac{I_n}{n !}+\frac{I_n-2}{(n-2) !}\right)$ equals
→
A point $P$ moves so that the sum of squares of its distances from the points $(1,2)$ and $(-2,1)$ is $14$ . Let $f(x, y)=0$ be the locus of $P$, which intersects the $x$-axis at the points $A , B$ and the $y-$axis at the point $C , D$. Then the area of the quadrilateral $ACBD$ is equal to.
→