Show that y= (1+x)-2 x 2+x , x>-1 is an increasing function on it… - Vidyadip

Question

Show that $y=\log (1+x)-\frac{2 x}{2+x}, x>-1$ is an increasing function on its domain.

✓

Answer

Get the step-by-step solution for this question inside the Vidyadip app.

Get the answer in the app

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 "Solve the Following Question.(4 Marks)" from Applications of Derivatives→Applications of Derivatives — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Solve the differential equation : $\frac{d y}{d x}+y \sec x=\tan x$.

If $\theta$ is the measure of the acute angle between the lines represented by the equation $a x^2+2 h x y+b y^2=0$, then prove that $\tan \theta=\left|\frac{2 \sqrt{h^2-a b}}{a+b}\right|$ where $a+b \neq 0$ and $b \neq 0$. Find the condition for colncident lines.

Maximize: $Z=6 x+4 y$
Subject to $x \leq 2, x+y \leq 3,-2 x+y \leq 1, x \geq 0, y \geq 0$. Also find maxdmum value of $Z$.

Solve the following differential equations:

$(x+y) \frac{d y}{d x}=1$

Find the Cartesian and vector equation of the plane which makes intercepts $1, 1, 1$ on the coordinate axes

If $x=\sqrt{a^{\sin ^{-1} t}}$ and $y=\sqrt{a^{\cos ^{-1 t}}}$, then show that $\frac{d y}{d x}=-\frac{y}{x}$.

Evaluate the following:

$\int_0^{\pi / 4} \frac{\cos 2 x}{1+\cos 2 x+\sin 2 x} d x$

A random variable $X$ has the following distribution :

$x$	0	1	2	3	4	5	6
$P ( X =x)$	$k$	$3k$	$5k$	$7k$	$9k$	$11k$	$13k$

(a) Find $k$,
(b) Find $P (0< X <4)$
(c) Obtain the cumulative distribution function (c.d.f.) of X.

Minimize $Z =4 x+5 y$
Subject to $2 x+y \geq 7,2 x+3 y \leq 15, x \leq 3, x \geq 0, y \geq 0$. Solve using graphical method.

Find the angles between the lines whose direction cosines $l, m, n$ satisfy the equations $5l + m + 3n = 0$ and $5mn − 2nl + 6lm = 0$