Calculus

Application of Derivatives

Medium

applied

The interval in which the function $f(x) = \log_e(2+x) - \frac{2x}{2+x}$ is increasing is

$[-2,\infty)$

$(2,\infty)$

$(-\infty,2)$

$(-\infty,-1]$

✅ Correct Option: 2

$f'(x) = \frac{1}{2+x} - \frac{4}{(2+x)^2} = \frac{x-2}{(2+x)^2}$ . The denominator is positive on the domain $x > -2$ , so $f'(x) > 0$ exactly when $x > 2$ , giving $(2,\infty)$ .

2026: 31 May Shift 2

The ordinate of the point on the curve $y^2 = 8x$ for which abscissa and ordinate change at the same rate is:

2026: 31 May Shift 2

The rate of change in area of a triangle having sides 10cm and 12cm when the variable angle between them at an angle $60°$ , is:

2025: 16 May Shift 1

Match List-I with List-II

Consider the function f(x) = 2x³ - 21x² + 36x + 80, x∈[0, 6]. Then

List-I	List-II
(A) one of its critical points is at x =	(I) -28
(B) Its absolute maximum value is	(II) -42
(C) Its absolute minimum value is	(III) 97
(D) Its second derivative at x = 0 is	(IV) 6

Choose the correct answer from the options given below:

2026: 21 May Shift 2

The interval in which the function $f(x) = x^2 - 3x + 7$ is increasing, is

2022: 17 Aug Shift 2

Based on above information answer the following question :

$\frac{dA(x)}{dx} =$

2025: 21 May Shift 1

The interval in which the function $f(x) = 2x^3 + 3x^2 - 12x + 1$ is strictly increasing, is

The interval in which the function f(x)=log⁡e(2+x)−2x2+xf(x) = \log_e(2+x) - \frac{2x}{2+x}f(x)=loge​(2+x)−2+x2x​ is increasing is

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The interval in which the function $f(x) = \log_e(2+x) - \frac{2x}{2+x}$ is increasing is