In general, two concave functions intersect at at most two points. True or False?

Keyla Koch

Keyla Koch

Answered question

2022-10-26

In general, two concave functions intersect at at most two points. True or False?

Answer & Explanation

Jean Deleon

Jean Deleon

Beginner2022-10-27Added 14 answers

It is not true in general that two concave functions intersect at at most two points. For example, the functions
f ( x ) = x 2 and g ( x ) = x 2 + sin x .
are both concave, with g ( x ) = 2 sin x < 1, but the graphs of f and g have infinitely many intersections.

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