Let f(x) be a function such that f'(a) 0. Then at x = a, f(x)

JEE Advanced Mathematics question

Mathematics Application of Derivatives JEE Advanced

Let be a function such that . Then at ,

(A)cannot have a maximum
(B)cannot have a minimum
(C)must have neither a maximum nor a minimum
(D)none of theseCorrect

Answer: (D)

Solution

If is an *interior* point of the domain and exists and is non-zero, Fermat's theorem says cannot have a local extremum at . Under that reading (c) would hold. However, the question puts no condition on . If is an **end point** of the domain, can have an

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Question ID VK-109407