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Problem 595

AMC 12 late, AIME early

Algebra Difficulty 5.0 Find the answer

(3) Let the function $f(x)=a|x|+\frac{b}{x}$ (where $a, b$ are constants), and $f(-2)=0$ , $f(x)$ has two intervals of monotonic increase. Find the relationship between $a$ and $b$ that satisfies the above conditions.

Your answer

Official solution

(3) $b=4a$ ( $a<0$ )

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.