Application of Derivatives Class 12 MCQs Questions with Answers

1. 2x³ – 6x + 5 is an increasing function, if

2. The slope of the tangent to the curve x = a sin t, y = a{cot t + log(tan t/2)} at the point ‘t’ is

3. The distance Y metres covered by a body in t seconds, is given by s = 3t² – 8t + 5. The body will stop after

4. Tangents to the curve x2 + y2 = 2 at the points (1, 1) and (-1, 1) are

5. If the volume of a sphere is increasing at a constant rate, then the rate at which its radius is increasing is

6. The tangent to the curve y = e2x at the point (0, 1) meets x-axis at

7. 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

8. The function f (x) = 1 – x³ – x5 is decreasing for

9. The function which is neither decreasing nor increasing in (π/2, 3π/2) is

10. The function f(x) = tan x – x

11. The function f(x) = cot-1 x + x increases in the interval

12. The function f(x) = log (1 + x) – 2x/2+x is increasing on

13. The function f(x) = 4 sin³ x – 6 sin²x + 12 sin x + 100 is strictly

14. Let the f: R → R be defined by f (x) = 2x + cos x, then f

15. If y = x4 – 10 and if x changes from 2 to 1.99 what is the change in y

16. If there is an error of a% in measuring the edge of a cube, then percentage error in its surface area is

17. If y = x3 + x2 + x + 1, then y

18. The function f(x) = x5 – 5×4 + 5×3 – 1 has

19. Find the maximum profit that a company can make, if the profit function is given by P(x) = 41 + 24x – 18×2.

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