What is the condition that f(x)=x^3+x^2+kx has no local extremum?

NDA 2021 Mathematics question

Mathematics Application of Derivatives NDA 2021

What is the condition that has no local extremum?

(A)
(B)Correct
(C)
(D)

Answer: (B)

Solution

. A local extremum occurs only where changes sign, which requires to have two distinct real roots, i.e. discriminant , or . So has no local extremum when , i.e. ;

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Question ID VK-033706