Q66.Let f : (−1, ∞) →R be defined by f(0) = 1 and f(x) = x1 loge(1 + x), x ≠0 . Then the function f (1) Decreases in (−1, 0) and increases in (0, ∞) (2) Increases in (−1, ∞) (3) Increases in (−1, 0) and decreases in (0, ∞) (4) Decreases in (−1, ∞)
What This Question Tests
This question requires finding the derivative of a piecewise function, analyzing its sign over the domain using L'Hopital's rule or series expansion for continuity at x=0, to determine its monotonicity.
Concepts Tested
Formulas Used
f'(x)
d/dx (log(1+x)/x)
Maclaurin series for log(1+x)
📚 NCERT Sections This Tests
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.
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.
1.1 — Define The Term Solution. How Many Types Of Solutions Are Formed? Write Briefly
Chemistry Class 11 · Chapter 1
1.1 Define the term solution. How many types of solutions are formed? Write briefly about each type with an example.
📋 Question Details
- Chapter
- Applications of Derivatives
- Topic
- Monotonicity of functions
- Year
- 2020
- Shift
- 02 Sep Shift 2
- Q Number
- Q66
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 6: Applications of Derivatives
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