Q81.Let f : R →R be defined by f(x) = {k2x−2x,+ 3, ifif xx ≤−1> −1 possible value of k is (1) 0 (2) −12 (3) −1 (4) 1
What This Question Tests
This question tests the understanding of continuity for piecewise functions and the conditions for a local extremum. Ensuring continuity at the critical point x=-1 leads to k=-1, but this value results in a local maximum rather than a local minimum, indicating a potential discrepancy in the problem statement, but k=-1 is the only value that ensures continuity.
Concepts Tested
Formulas Used
Conditions for continuity at a point
First derivative test for extrema
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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.
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📋 Question Details
- Chapter
- Applications of Derivatives
- Topic
- Maxima and Minima, Continuity
- Year
- 2010
- Shift
- Unknown
- Q Number
- Q81
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 5: Continuity and Differentiability
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