MCQs of Applications of Derivatives

Applications of Derivatives MCQs

MCQs of Applications of Derivatives

Showing 111 to 120 out of 152 Questions

111.

The point on the parabola y² = 8x such that

\frac{d x}{d t} = \frac{d y}{d t}

is _____.

(a)	(0, 0)
(b)	$(\frac{1}{2}, 2)$
(c)	(4, 2)
(d)	(2, 4)

112.

Volume of a cube increases at a constant rate of 3 cm³/sec. The rate of increase of its surface area is _____, when its side is 10 cm.

(a)	3.6 cm²/sec.
(b)	0.12 cm²/sec.
(c)	1.2 cm²/sec.
(d)	0.36 cm²/sec.

113.

The local maximum value for f(x) = x³ - 12x is _____.

(a)	8
(b)	12
(c)	0
(d)	16

114.

If p and q are positive real numbers such that p² + q² = 1, then maximum value of p + q is _____.

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

115.

The function f(x) = cot^-1x + x increases in the interval _____.

(a)	(1, ∞)
(b)	(-1, ∞)
(c)	(-∞, ∞)
(d)	(0, ∞)

116.

The greatest value of

f (x) = {(x + 1)}^{\frac{1}{3}} - {(x - 1)}^{\frac{1}{3}}

on [0, 1] is _____.

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

117.

If the function f(x) = 2x³ - 9ax² + 12a²x + 1 attains it maximum and minimum at p and q respectively such that p² = q, then q equals _____ .

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

118.

A point on the parabola y² = 18x at which the ordinate increases at twice the rate of abscissa is ______.

(a)	$(- \frac{9}{8}, \frac{9}{2})$
(b)	$(\frac{9}{8}, \frac{9}{2})$
(c)	(2, -4)
(d)	(2, 4)

119.

A triangle park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length x. The maximum area enclosed by the park is _____.

(a)	${πx}^{2}$
(b)	$\frac{3}{2} x^{2}$
(c)	$\sqrt{\frac{x^{3}}{8}}$
(d)	$\frac{1}{2} x^{2}$

120.

The function f(x) = tan^-1 (sinx + cosx) is an increasing function in _____.

(a)	$(0, \frac{π}{2})$
(b)	$(- \frac{π}{2}, \frac{π}{2})$
(c)	$(\frac{π}{4}, \frac{π}{2})$
(d)	$(- \frac{π}{2}, \frac{π}{4})$

Showing 111 to 120 out of 152 Questions