Data-Structures
January 26, 2024GATE 1995
January 26, 2024TIFR PHD CS & SS 2020
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Question 8
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Consider a function f : [0, 1] –> [0, 1] which is twice differentiable in (0, 1). Suppose it has exactly one global maximum and exactly one global minimum inside (0, 1). What can you say about the behaviour of the first derivative f’ and and second derivative f” on (0, 1) (give the most precise answer)?
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f’ is zero at exactly two points, f” need not be zero anywhere
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f’ is zero at exactly two points, f” is zero at exactly one point
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f’ is zero at at least two points, f” is zero at exactly one point
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f’ is zero at at least two points, f” is zero at at least one point
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f’ is zero at at least two points, f” is zero at at least two points
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Correct Answer: D