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Q#1
Calculus
GATE EE 2024
MCQ
+2 marks
-0.66 marks
Let 
be a real-valued function whose second derivative is positive for 
. Which of the following statements is/are always true?
has at least one local minimum.
cannot have two distinct local minima.
has at least one local maximum.
The minimum value of cannot be negative.
Explanation:
This means the f’(t) is a monotonically increasing function.
Hence, f’(t) can be zero at most once and hence there can only be at most one local minima.
Since, double derivative is always positive so we cannot comment on local maxima.
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