GATE CE 2018 Set 1 — Question 13
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Engineering Mathematics → Calculus → Local Maxima & Minima
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Question
At the point , the function has
Correct answer
(D) neither local maximum nor local minimum
Solution
To find the nature of the function at :
1.Find the first derivative: . At , . This is a stationary point.
2.Find the second derivative: . At , . The second derivative test is inconclusive.
3.Find the third derivative: . At , .
Since the first non-zero derivative at the stationary point is of odd order (3rd order), the point is a point of inflection, not a local extremum. Therefore, it has neither a local maximum nor a local minimum.Continue learning with Success Tracker
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