MCQs of Applications of Derivatives

Applications of Derivatives MCQs

MCQs of Applications of Derivatives

Showing 171 to 180 out of 266 Questions

171.

The radius of a right circular cone is constant. If there is an error δh in measuring its height, the error in the measurement of its volume is ______.

(a)	$\frac{2}{3} πr δ h$
(b)	$\frac{1}{3} {πr}^{2} δh$
(c)	$\frac{1}{3} πr δ h$
(d)	None of the above

172.

Find the point on y = x³ where the tangent of slope is equal to the y co-ordinate of the point.

(a)	(-3, -27)
(b)	(1, 1)
(c)	(3, 27)
(d)	(27, 3)

173.

What is the approximate value of tan 44° ? (using differentiation)

(a)	$\frac{π}{90} + 1$
(b)	$\frac{π}{90} - 1$
(c)	$- \frac{π}{90} - 1$
(d)	$1 - \frac{π}{90}$

174.

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, ∞)

175.

The slope of the normal to x² = 4y at (1, 2) is _____.

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

176.

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

177.

For the real function f,

f' (x) = \sqrt{x^{2} + 12}, \forall x \in R

and f(2) = 4, then the approximate value of f(1.99) is _____.

(a)	3.6
(b)	4.04
(c)	4.4
(d)	3.96

178.

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

179.

Tangent at any point to the curve y = 7x² + 7x + 7 is _____.

(a)	parallel to Y - axis
(b)	makes acute angle with positive X - axis
(c)	makes obtuse angle with positive X - axis
(d)	parallel to X - axis

180.

The equation of tangent to

y = e^{x}

at (0, 1) is _____.

(a)	x - y + 1 = 0
(b)	x + y - 1 = 0
(c)	x - y - 1 = 0
(d)	x + y + 1 = 0

Showing 171 to 180 out of 266 Questions