MCQs of Applications of Derivatives

Applications of Derivatives MCQs

MCQs of Applications of Derivatives

Showing 91 to 100 out of 152 Questions

91.

If A > 0, B > 0 and A + B =

\frac{π}{3}

then maximum value of tan A . tan B is _____

(a)	$\frac{1}{3}$
(b)	1
(c)	3
(d)	2

92.

For a function f if f '(2) = 0 = f''(2) and f(x) has local maximum value at x = 2 is -17 then f(x) = _____ .

(a)	(x - 2)⁴
(b)	3 - (x - 2)⁴
(c)	-17 - (x - 2)⁴
(d)	none

93.

The radius of a circular metal plate when heated, increases by 2%. If its radius is 10 cm, then the increase in its area is _____.

(a)	4π cm²
(b)	4π cm
(c)	20π cm²
(d)	2π cm²

94.

The rate of change of the volume of a sphere having radius r with respect to its surface area is _____

(a)	8πr
(b)	4πr²
(c)	$\frac{r}{2}$
(d)	$\frac{2}{r}$

95.

A function

f (x) = e^{\frac{1}{x}}, x \neq 0

is _____ function.

(a)	a decreasing
(b)	an increasing
(c)	increasing and decreasing
(d)	None of the above

96.

f : R→R, f(x) = x² + 6x + 15 is _____

(a)	strictly decreasing function in (3, ∞)
(b)	strictly decreasing function in (-3, ∞)
(c)	strictly increasing function in (-∞, 3)
(d)	strictly increasing function in (-3, ∞)

97.

How many extreme values of f(x) = x + 2 sinx,

x \in (- \frac{π}{2}, \frac{π}{2})

are there ?

(a)	0
(b)	1
(c)	2
(d)	4

98.

The local maximum value of

f (x) = x - \frac{1}{x}, x \neq 0

is _____.

(a)	-2
(b)	4
(c)	Does not exist
(d)	2

99.

The rate of change of surface area of a sphere w.r.t. time is 16π cm²/sec. Find the rate of the change in its volume with to time at the moment when the radius is 2 cm.

(a)	32
(b)	8
(c)	16
(d)	4

100.

The rate of change of volume of sphere with respect to its surface area S is _____ .

(a)	$4 \sqrt{\frac{s}{π}}$
(b)	$\sqrt{\frac{s}{π}}$
(c)	$\frac{1}{2} \sqrt{\frac{s}{π}}$
(d)	$\frac{1}{4} \sqrt{\frac{s}{π}}$

Showing 91 to 100 out of 152 Questions