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JEE Math Practice Question

If the functions $f(x)=\frac{x^3}{3}+2 b x+\frac{a x^2}{2}$ and $g(x)=\frac{x^3}{3}+a x+b x^2, a \neq 2 b$ have a common extreme point, then $a+2 b+7$ is equal to :

  1. A.6
  2. B.$\frac{3}{2}$
  3. C.3
  4. D.4

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