MCQs of Applications of Derivatives

Showing 131 to 140 out of 266 Questions

131.

Let C be a curve given by

y = 1 + \sqrt{4 x - 3}, x > \frac{3}{4}

If P is a point on C, such that the tangent at P has slope

\frac{2}{3}

, then a point through which the normal at P passes, is :

132.

Let

f (x) = \sin^{4} x + \cos^{4} x

, Then f is increasing function in the interval :

133.

log

|\sin x|

is _____ function on

(0, \frac{π}{3})

134.

Equation of the tangent to xⁿ + yⁿ = 2 at point (1, 1) is _____ .

135.

Slope of a tangent to y = x² - 4x + 5 at the point _____ is 4.

136.

Rate of increase of the area of a square w.r.t its perimeter is _____ (l = length of a side of the square).

137.

If kx³ - 9x² + 9x + 3 is an increasing function on R then _____ .

138.

If 3x - y = 1 is an equation of a tangent to a curve y = ax² + bx at (1, 2) then _____ .

139.

Water is falling into a cylinder of radius 1 m at the rate of 1 m³/min. Then rate of increase of height of the surface is _____

140.

A line

\frac{x}{a} + \frac{y}{b} = 1

touches the curve

y = b e^{- \frac{x}{a}}

at a point _____

Showing 131 to 140 out of 266 Questions