Suppose f(x) is a function from R to R and f is strictly quasi-concave. If x^∗ is a point such that f′(x^∗)=0, then can we say that x^∗ is a global maximum of this function? What about local maximum then?

Kareem Mejia

Kareem Mejia

Answered question

2022-11-05

Suppose f ( x ) is a function from R to R and f is strictly quasi-concave. If x is a point such that f ( x ) = 0, then can we say that x is a global maximum of this function? What about local maximum then?

Answer & Explanation

Jackson Trevino

Jackson Trevino

Beginner2022-11-06Added 14 answers

Take f ( x ) = ( sgn x ) x 2 . Then f is strictly monotonic (hence strictly quasi-convex) and f ( 0 ) = 0, but f has no local max or min.

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