# Application of Derivatives

This is an MCQ-based quiz on the Application of Derivatives.

This includes the Rate of Change of Quantities, Increasing and Decreasing Functions, Tangents, Normals, Approximations, Maxima,and Minima.

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The sides of an equilateral triangle are increasing at the rate of 2cm/sec. The rate at which the are increases, when side is 10 cm is

10 cm²/s √3 cm²/s 10√3 cm²/s 10/3 cm²/s

The equation of normal to the curve 3x² – y² = 8 which is parallel to the line ,x + 3y = 8 is

3x – y = 8 3x + y + 8 = 0 x + 3y ± 8 = 0 x + 3y = 0

If the curve ay + x² = 7 and x³ = y, cut orthogonally at (1, 1) then the value of a is

1 0 -6 6

A ladder, 5 meter long, standing oh a horizontal floor, leans against a vertical wall. If the top of the ladder slides downwards at the rate of 10 cm/sec, then the rate at which the angle between the floor and the ladder is decreasing when lower end of ladder is 2 metres from the wall is

The total revenue received from the sale of x units of a product is given by R (x) = 3x² + 36x + 5. The marginal revenue, when x = 15 is:

116 96 90 126.

The interval in which y = x² e-x is increasing with respect to x is:

(-∞, ∞) (-2,0) (2, ∞) (0, 2).

The slope of the normal to the curve y = 2x² + 3 sin x at x = 0 is

3 1/3 -3 –1/3

The line y = x + 1 is a tangent to the curve y² = 4x at the point:

(1, 2) (2, 1) (1, -2) (-1, 2).

If f(x) = 3x² + 15x + 5, then the approximate value of f(3.02) is:

47.66 57.66 67.66 77.66.

The smallest value of the polynomial x³ – 18x² + 96x in [0, 9] is

126 0 135 160

The function f(x) = tan x – x

Always increases

Always decreases

Sometimes increases and sometimes decreases

Never increases

The function f(x) = 2x³ – 3x² – 12x + 4 has

Two points of local maximum

Two points of local minimum

One maxima and one minima

No maxima or minima

The curve y – x^1/5 at (0, 0) has

A vertical tangent (parallel to y-axis)

A horizontal tangent (parallel to x-axis)

An oblique tangent

No tangent

If x is real, the minimum value of x² – 8x + 17 is

-1

0

1

2

Maximum slope of the curve y = -x³ + 3x² + 9x – 27 is

0

12

16

32

Quiz/Test Summary
Title: Application of Derivatives
Questions: 15
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