Q87.Let f and g be twice differentiable even functions on (−2, 2) such that f( 41 ) = 0, f( 21 ) = 0, f(1) = 1 and g( 34 ) = 0, g(1) = 2 Then, the minimum number of solutions of f(x)g′′(x) + f ′(x)g′′(x) = 0 in (−2, 2) is equal to _____.
What This Question Tests
This question applies Rolle's Theorem multiple times and requires recognizing an identity involving derivatives, alongside using the properties of even functions to find roots.
Concepts Tested
Formulas Used
(fg)' = f'g + fg'
Rolle's Theorem condition
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📋 Question Details
- Chapter
- Applications of Derivatives
- Topic
- Rolle's Theorem
- Year
- 2022
- Shift
- 29 Jun Shift 2
- Q Number
- Q87
- Type
- Numerical
- NCERT Ref
- Class 12 Mathematics Ch 6: Application of Derivatives
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