Q73.Let f : R →R be defined as f(x) = { −43 x3 +3xex2x2 + 3x,, xx >≤00 . Then f is increasing function in the interval (1) (−12 , 2) (2) (0, 2) (3) (−1, 23 ) (4) (−3, −1) , α ∈R where [x] is the greatest integer less than or equal to x, then the value of
What This Question Tests
This question involves finding the intervals where a piecewise function is increasing by calculating its derivative for each piece and analyzing its sign.
Concepts Tested
Formulas Used
f'(x) > 0 for increasing function
📚 NCERT Sections This Tests
3.23 — The Rate Constant For The Decomposition Of Hydrocarbons Is 2.418 × 10–5S–1
Chemistry Class 11 · Chapter 3
3.23 The rate constant for the decomposition of hydrocarbons is 2.418 × 10–5s–1 at 546 K. If the energy of activation is 179.9 kJ/mol, what will be the value of pre-exponential factor.
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.
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.
📋 Question Details
- Chapter
- Applications of Derivatives
- Topic
- Increasing/Decreasing functions
- Year
- 2021
- Shift
- 22 Jul Shift 1
- Q Number
- Q73
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 6: Application of Derivatives
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