Question

Let $x=2$ be a local minima of the function $f(x)=2 x^4-18 x^2+8 x+12$, $x \in(-4,4)$ If $M$ is local maximum value of the function $f$ in $(-4,4)$, then $M =$

• A. $18 \sqrt{6}-\frac{33}{2}$
• B. $12 \sqrt{6}-\frac{33}{2}$
• C. $12 \sqrt{6}-\frac{31}{2}$
• D. $18 \sqrt{6}-\frac{31}{2}$

Answer 1

Answer: (B)

$12 \sqrt{6}-\frac{33}{2}$

Answer 2

f′(x)=8x3−36x+8=4(2x3−9x+2)
f′(x)=0
∴x=26​−2​
Now
f(x)=(x2−2x−29​)(2x2+4x−1)+24x+7.5
∴f(26​−2​)=M=126​−233​