The interval for which the function f(x)=x/(x^2+x+1) is an increasing function, is: Option 1: (0,∞) Option 2: (-∞,-1)(1,∞) Option 3: (-1,1) Option 4: (-∞,0)

Answer: (-1,1). Solution: f'(x)=((x^2+x+1)-x(2x+1))/((x^2+x+1)^2)=(1-x^2)/((x^2+x+1)^2). The denominator is always positive, so f'(x)>0 exactly when 1-x^2>0, i.e. on (-1,1).

Calculus

Application of Derivatives

Easy

common

The interval for which the function $f(x)=\frac{x}{x^2+x+1}$ is an increasing function, is:

$(0,\infty)$

$(-\infty,-1)\cup(1,\infty)$

$(-1,1)$

$(-\infty,0)$

✅ Correct Option: 3

$f'(x)=\frac{(x^2+x+1)-x(2x+1)}{(x^2+x+1)^2}=\frac{1-x^2}{(x^2+x+1)^2}$ .

The denominator is always positive, so $f'(x)>0$ exactly when $1-x^2>0$ , i.e. on $(-1,1)$ .

2026: 19 May Shift 2

The interval in which the function $f(x) = -x^2 - 2x + 18$ is decreasing is :

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If $f(x)=2\left(\tan ^{-1}\left(e^{x}\right)-\frac{\pi}{4}\right)$ , then $f(x)$ is :

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A balloon which always remains spherical is being inflated by pumping in 900 cubic cm of gas per second. The rate at which the radius of the balloon increases when the radius is 15 cm is

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The rate of change of the area of a circular disc with respect to its circumference when radius is 3 is :

2026: 15 May Shift 1

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	$y = x^2$	I.	decreasing on $(0, \infty)$
B.	$y = -x^2$	II.	increasing on $(0, \infty)$
C.	$y = x$	III.	decreasing on $(-\infty, \infty)$
D.	$y = -x$	IV.	increasing on $(-\infty, \infty)$

Choose the correct answer from the options given below:

2026: 26 May Shift 2

The volume of a cube is increasing at the rate 9 $cm^3/s$ . How fast is the surface area increasing when the length of an edge is 10 cm ?

The interval for which the function f(x)=xx2+x+1f(x)=\frac{x}{x^2+x+1}f(x)=x2+x+1x​ is an increasing function, is:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The interval for which the function $f(x)=\frac{x}{x^2+x+1}$ is an increasing function, is: