Calculus

Application of Derivatives

Easy

applied

If an edge of a variable cube is increasing at the rate of 0.8 cm/sec, at what rate its surface area is increasing when its edge is 10 cm?

72 cm²/sec

96 cm²/sec

48 cm²/sec

90 cm²/sec

✅ Correct Option: 2

Surface area of a cube is $S = 6a^2$ , so $\dfrac{dS}{dt} = 12a\dfrac{da}{dt}$ .

Substituting $a = 10$ and $\dfrac{da}{dt} = 0.8$ :

$\dfrac{dS}{dt} = 12(10)(0.8) = 96$ cm²/sec.

2026: 19 May Shift 1

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

2026: 29 May Shift 1

The local maximum value of the function $f(x)=\dfrac{b^2}{a^4}(a^2x^2-x^4), a,b>0$ is equal to:

2025: 29 May Shift 2

Match List-I with List-II

List-I	List-II
Function f(x)	Interval for increasing/decreasing of function f(x)
---	---
(A) $f(x) = x\vert x\vert$	(I) Decreases on $(0, \infty)$
(B) $f(x) = x^2 + 2x - 5$	(II) Increases on $(3, \infty)$
(C) $f(x) = x^2 - 6x + 9$	(III) Decreases on $(-\infty, -1)$
(D) $f(x) = -x^2$	(IV) Increases on $(-\infty, \infty)$

Choose the correct answer from the options given below:

2025: 2 June Shift 1

The function $f(x) = 2\log_e(x-2) - x^2 + 4x + 1, (x > 2)$ is increasing on the interval:

2025: 14 May Shift 1

The rate of change of area of a circle with respect to its circumference when radius is 4cm, is

2025: 14 May Shift 1

If the maximum value of the function $f(x) = \frac{\log_ex}{x}$ , $x > 0$ occurs at $x = a$ , then $a^2f''(a)$ is equal to

Solution