MCQs of Applications of Derivatives

Applications of Derivatives MCQs

MCQs of Applications of Derivatives

Showing 211 to 220 out of 266 Questions

211.

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)	$\frac{1}{3}$

212.

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

213.

The normal to the curve x = a(1 + cosθ), y = a sinθ at θ always passes through the fixed point _____ .

(a)	(a, a)
(b)	(a , 0)
(c)	(0, a)
(d)	None of the above

214.

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)

215.

The normal to the curve x = a (cosθ + θ sinθ), y = a(sinθ - θ cosθ) at any θ is such that _____ .

(a)	it makes a constant angle with X - axis
(b)	it passes through the origin
(c)	it is at a constant distance from the origin
(d)	None of the above

216.

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)	$\frac{1}{2} x^{2}$

217.

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)	$(- \frac{π}{2}, \frac{π}{4})$

218.

The equation of the tangent to the curve

y = x + \frac{4}{x^{2}}

that is parallel to the X - axis, is ______ .

(a)	y = 2
(b)	y = 3
(c)	y = 0
(d)	y = 1

219.

A spherical balloon is filled with 4500π cubic meter of helium gas. If a leak in the balloon causes the gas to escape at the rate of 72π cubic metre/minute, the rate (in metres per minute) at which the radius of the balloon decreases 49 minutes after the leakage begins is _____ metre/minute.

(a)	$\frac{9}{7}$
(b)	$\frac{7}{9}$
(c)	$\frac{2}{9}$
(d)	$\frac{9}{2}$

220.

On the interval [0, 1] the function x²⁵(1 - x)⁷⁵ takes its maximum value at the point x = _____.

(a)	0
(b)	$\frac{1}{4}$
(c)	$\frac{1}{2}$
(d)	$\frac{1}{3}$

Showing 211 to 220 out of 266 Questions