Q64.Let the function , f : [−7, 0] →R be continuous on [−7, 0] and differentiable on (−7, 0). If f(−7) = −3 and f '(x) ≤2 for all x ∈(−7, 0), then for all such functions f, f(−1) + f(0) lies in the interval (1) (−∞, 20] (2) [−3, 11] (3) (−∞, 11] (4) [−6, 20]
What This Question Tests
This question tests the application of Lagrange's Mean Value Theorem on different intervals to establish upper bounds for the function values, which are then summed to find the required interval.
Concepts Tested
Formulas Used
f'(c) = (f(b) - f(a)) / (b - a)
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📋 Question Details
- Chapter
- Applications of Derivatives
- Topic
- Mean Value Theorem
- Year
- 2020
- Shift
- 07 Jan Shift 1
- Q Number
- Q64
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 6: Applications of Derivatives
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