Q71.The function f(x) = xex(1−x), x ∈R, is (1) increasing in (−12 , 1) (2) decreasing in ( 12 , 2) (3) increasing in (−1, −12 ) (4) decreasing in (−12 , 12 )
What This Question Tests
This question requires finding the first derivative of the given function and analyzing its sign to determine the intervals where the function is increasing or decreasing.
Concepts Tested
Formulas Used
f'(x) > 0 for increasing function
f'(x) < 0 for decreasing function
d/dx (uv) = u'v + uv'
📚 NCERT Sections This Tests
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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.
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📋 Question Details
- Chapter
- Applications of Derivatives
- Topic
- Monotonicity of functions
- Year
- 2022
- Shift
- 28 Jul Shift 2
- Q Number
- Q71
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 6: Applications of Derivatives
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