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Class 12 Mathematics: Application of Derivatives
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MCQs on derivative application, quantities rate change, derivative applications for error determination, increasing and decreasing functions, tangents, normals, approximations, maxima and minima.

Class 12 Mathematics: Application of Derivatives
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25 Questions

1. What will be the approximate change in the surface area of a cube of side xm caused by increasing the side by 2%.
2. A ladder 20 ft long leans against a vertical wall. If the top end slides downwards at the rate of 2ft per second, what will be the rate at which the slope of the ladder changes?
3. What will be the differential function of √(x2 + 2)?
4. What will be the average rate of change of the function [y = 16 – x2] between x = 3 and x = 4?
5. What is the relation between f(x) and ℓ when the maximum value or greatest value function f is defined on a set A and ℓ ∈ f(A)?
6. A 5 ft long man walks away from the foot of a 12(½) ft high lamp post at the rate of 3 mph. What will be the rate at which the shadow increases?
7. Find the points on the curve y=3x4+2x3-1 at which the tangents is parallel to the x-axis.
8. What will be the increment of the differentiable function f(x) = 2x2 – 3x + 2 when x changes from 3.02 to 3?
9. Find the equation of the tangent of the tangent to the curve 2x2+3y2=3 at the point(3,4).
10. Find the tangent to the curve y=5x4-3x2+2x-1 at x=1.
11. Find the approximate value of (82)1/4.
12. What is the mathematical expression for a function to be strictly decreasing on (a,b)?
13. If log103 = 0.4771 and log10e = 0.4343, then what is the value of log1030.5?
14. Find the interval in which function f(x) = sinx+cosx, 0 ≤ x ≤ 2π is decreasing.
15. What is the condition for a function f to be decreasing if f be continuous and differentiable on (a,b)?
16. Find the approximate value of (127)1/3.
17. A solid cube changes its volume such that its shape remains unchanged. For such a cube of unit volume, what will be the value of rate of change of volume?
18. The length of a side of a cube is 10cm; if an error of 0.05cm is made in measuring the side, then what is the value of approximate error in calculating its volume?
19. Find the approximate value of f(5.03), where f(x)=4x2-7x+2.
20. The rate of change of area of a square is 40 cm2/s. What will be the rate of change of side if the side is 10 cm.
21. Find the intervals in which f(x) = x2 + 2x – 5 is strictly increasing.
22. Find the approximate change in the volume of cube of side xm caused by increasing the side by 6%.
23. Find the slope of the normal to the curve y=4x2-14x+5 at x=5.
24. The edge of a cube is increasing at a rate of 7 cm/s. Find the rate of change of area of the cube when x=6 cm.
25. Find the approximate value of f(4.04), where f(x)=7x3+6x2-4x+3.

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