MCQs of Applications of Derivatives

Applications of Derivatives MCQs

MCQs of Applications of Derivatives

Showing 11 to 20 out of 152 Questions

11.

The minimum value of

f (x) = 3 \cos x + 4 \sin x

is ______

(a)	7
(b)	5
(c)	-5
(d)	4

12.

f (x) = x \log x

has minimum value _____

(a)	1
(b)	0
(c)	e
(d)	$- \frac{1}{e}$

13.

f (x) = \sqrt{3} \cos x + \sin x, x \in [0, \frac{π}{2}]

is maximum for x= _____

(a)	$\frac{π}{6}$
(b)	$\frac{π}{3}$
(c)	$\frac{π}{2}$
(d)	0

14.

f (x) = (x - a)^{2} + (x - b)^{2} + (x - c)^{2}

has minimum value at x = _____

(a)	$\sqrt[3]{a b c}$
(b)	$a + b + c$
(c)	$\frac{a + b + c}{3}$
(d)	0

15.

f (x) = (x + 2) e^{- x}

is increasing in _____

(a)	$(- \infty, - 1)$
(b)	$(- 1, - \infty)$
(c)	$(2, \infty)$
(d)	$R^{+}$

16.

A cone with its height equal to the diameter of the base is expanding in volume at the rate of

50 c m^{3} / s e c

. If the base has area

1 m^{2}

, the radius is increasing at the rate _____

(a)	0.0025 cm/sec
(b)	0.25 cm/sec
(c)	1 cm/sec
(d)	4 cm/sec

17.

The rate of increaing of

f (x) = x^{3} - 5 x^{2} + 5 x + 25

is twice the rate of increase of x for x = _____.

(a)	$- 3, - \frac{1}{3}$
(b)	$3, \frac{1}{3}$
(c)	$- 3, \frac{1}{3}$
(d)	$3, - \frac{1}{3}$

18.

The radius of a cone increases at the rate of 4 cm/sec and the altitude is decreasing at the rate of 3 cm/sec. When the radius is 3 cm and altitude is 4 cm, the rate of change of lateral surface is _____.

(a)	$30 π c m^{2} / s e c$
(b)	$10 c m^{2} / s e c$
(c)	$20 π c m^{2} / s e c$
(d)	$22 π c m^{2} / s e c$

19.

The rate of change of surface area of a sphere w.r.t. radius is _____

(a)	$8 π (diameter)$
(b)	$3 π (diameter)$
(c)	$4 π (radius)$
(d)	$8 π (radius)$

20.

The rate of change of volume of a cylinder w.r.t. radius whose radius is equal to its height is _____.

(a)	4 (area of base)
(b)	3 (area of base)
(c)	2 (area of base)
(d)	(area of base)

Showing 11 to 20 out of 152 Questions