MCQs of Applications of Derivatives

Showing 71 to 80 out of 266 Questions

71.

f (x) = x^{2} + a x + 5

is increasing on (2, 3), then minimum value of a ∈ R is _____

72.

f (x) = \{\begin{cases} 0, & x = 0 \\ x - 3, & x > 0 \end{cases}

then f(x) is

(a)	increasing for $x \geq 0$
(b)	strictly increasing for x > 0
(c)	strictly increasing for x = 0
(d)	not continuous at x = 0 so it is not increasing for x > 0

73.

f (x) = \frac{λ \sin x + 6 \cos x}{2 \sin x + 3 \cos x}

is strictly increasing function, then

74.

Function

f (x) = 1 - e^{- \frac{x^{2}}{2}}

(a)	increasing for all x ∈ R
(b)	decreasing for all x ∈ R
(c)	decreasing for x < 0 and increasing for x > 0
(d)	increasing for x < 0 and decreasing for x > 0

75.

f (x) = x e^{1 - x}

then f is _____

(a)	strictly increasing function in $(\frac{1}{2}, 2)$
(b)	increasing function in (0, ∞)
(c)	decreasing function in (0, 2)
(d)	strictly decreasing function in (1, ∞)

76.

f (x) = \cos x + b x + c

is increasing function on R then,

77.

If line ax + by + c = 0 is tangent to curve xy = 4 then _____

78.

Distance of normal at x = 0 of

y = e^{2 x} + x^{2}

from origin is _____

79.

If curves

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{12} = 1

and y³ = 8x intersect orthogonaly then a² = _____

80.

Length of sub-interval at t-point of curve

x = a (t + \sin t), y = a (1 - \cos t)

is _____

Showing 71 to 80 out of 266 Questions