Q73.Consider the function f : R →R defined by f(x) = { (2 −sin(0, x1 )) x , xx =≠00 (1) monotonic on (−∞, 0) ∪(0, ∞) (2) not monotonic on (−∞, 0) and (0, ∞) (3) monotonic on (0, ∞) only (4) monotonic on (−∞, 0) only
What This Question Tests
This question asks about the monotonicity of a piecewise function defined using sin(1/x). It requires calculating the derivative and analyzing its sign in different intervals, especially around the point of discontinuity, testing conceptual understanding rather than just computation.
Concepts Tested
Formulas Used
f'(x) > 0 for strictly increasing
f'(x) < 0 for strictly decreasing
Derivatives of trigonometric functions
📚 NCERT Sections This Tests
9.15 — Apply Mirror Equation And The Condition:
Physics Class 12 · Chapter 9
9.15 Apply mirror equation and the condition: (a) f < 0 (concave mirror); u < 0 (object on left) (b) f > 0; u < 0 (c) f > 0 (convex mirror) and u < 0 (d) f < 0 (concave mirror); f < u < 0 to deduce the desired result.
1.3 — Define The Following Terms:
Chemistry Class 11 · Chapter 1
1.3 Define the following terms: (i) Mole fraction (ii) Molality (iii) Molarity (iv) Mass percentage.
14.2 — Which Of The Statements Given In Exercise 14.1 Is True For P-Type
Physics Class 12 · Chapter 14
14.2 Which of the statements given in Exercise 14.1 is true for p-type semiconductos.
📋 Question Details
- Chapter
- Applications of Derivatives
- Topic
- Monotonicity of functions
- Year
- 2021
- Shift
- 17 Mar Shift 2
- Q Number
- Q73
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 6: Applications of Derivatives
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