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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 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
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
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
1/10 radian/sec
1/20 radian/sec
20 radian/sec
10 radian/sec
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:
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
