Q73.Let g(x) = 3f x + f(3 - x) and f" (x) > 0 for all x ∈( 0, 3 ) . If g is decreasing in ( 0, α ) and increasing in 3 ( α, 3 ) , then 8α is (1) 24 (2) 0 (3) 18 (4) 20
What This Question Tests
This question tests the application of the first derivative test to determine the intervals of monotonicity for a function 'g(x)' defined in terms of another function 'f(x)'.
Concepts Tested
Formulas Used
g'(x) < 0 for decreasing, g'(x) > 0 for increasing
📚 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.
3.25 — Sucrose Decomposes In Acid Solution Into Glucose And Fructose According
Chemistry Class 11 · Chapter 3
3.25 Sucrose decomposes in acid solution into glucose and fructose according to the first order rate law, with t1/2 = 3.00 hours. What fraction of sample of sucrose remains after 8 hours ?
3.18 — For A First Order Reaction, Show That Time Required For 99% Completion
Chemistry Class 11 · Chapter 3
3.18 For a first order reaction, show that time required for 99% completion is twice the time required for the completion of 90% of reaction.
📋 Question Details
- Chapter
- Applications of Derivatives
- Topic
- Monotonicity of functions
- Year
- 2024
- Shift
- 27 Jan Shift 2
- Q Number
- Q73
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 6: Applications of Derivatives
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