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Let $f(x) = ax^2 - b |x|$, where $a$ and $b$ are constants. Then at $x=0, f(x)$ is, 

  1. maximized whenever $a>0, b>0$
  2. maximized whenever $a>0, b<0$
  3. minimized whenever $a>0, b>0$
  4. minimized whenever $a>0, b<0$
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