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.

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

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

1/10 radian/sec

1/20 radian/sec

20 radian/sec

10 radian/sec

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

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

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

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

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

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