If $a x^2+b x+c < 0 \forall x \in \mathbb{R}$ and the expressions $c x^2+a x+b$ and $a x^2+b x+c$ have their extreme values at the same point $x$, then for the expression $c x^2+a x+b$

• A

  Minimum value $=\frac{4 b}{3}$
• B

  Maximum value $=\frac{4 a}{3}$
• C

  Minimum value $=\frac{3 a}{4}$
• Correct answer
  D

  Maximum value $=\frac{3 \mathrm{~b}}{4}$

Hence, the correct answer is option: 'D'.