Q73.Let f : R →R be a function defined by f(x) = (x −3)n1(x −5)n2, n1, n2 ∈N . The, which of the following is NOT true? (1) For n1 = 3, n2 = 4 , there exists α ∈(3, 5) (2) For n1 = 4, n2 = 3, there exists α ∈(3, 5) where f attains local maxima. where f attains local maxima. (3) For n1 = 3, n2 = 5 , there exists α ∈(3, 5) (4) For n1 = 4, n2 = 6, there exists α ∈(3, 5) where f attains local maxima. where f attains local maxima.
What This Question Tests
This question tests the understanding of local maxima using the first derivative test. It requires calculating the derivative of the given function and analyzing its sign change around critical points for different values of n1 and n2.
Concepts Tested
Formulas Used
f'(x) = 0 for critical points
Sign change of f'(x) for local maxima/minima
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📋 Question Details
- Chapter
- Applications of Derivatives
- Topic
- Local maxima and minima
- Year
- 2022
- Shift
- 29 Jun Shift 2
- Q Number
- Q73
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 6: Application of Derivatives
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