Q80.If f(x) = xex(1−x), x ∈R, then f(x) is (1) decreasing on [−1/2, 1] (2) decreasing on R (3) increasing on [−1/2, 1] (4) increasing on R
What This Question Tests
This question assesses the ability to determine intervals where a function is increasing or decreasing by computing its first derivative and analyzing its sign using critical points.
Concepts Tested
Formulas Used
(uv)' = u'v + uv'
f'(x) > 0 for increasing
f'(x) < 0 for decreasing
📚 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.
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.
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.
📋 Question Details
- Chapter
- Applications of Derivatives
- Topic
- Monotonicity of a function
- Year
- 2012
- Shift
- 12 May Online
- Q Number
- Q80
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 6: Applications of Derivatives
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