Verified Solution • 2025–26 Session moderate

QJEEM23Ma7453: JEE Main 2023 Mathematics - Class 12 JEEM23Ma7453 Solution: Let be a local minima of the function . If M is local maximum…

Let x=2x=2 be a local minima of the function f(x)=2x4−18x2+8x+12,x∈(−4,4)f(x)=2x^4-18x^2+8x+12,x\in(-4,4) . If M is local maximum value of the function ff in ( −4,4)-4,4) , then M =

Multiple Choice Options

  • A 186−33218\sqrt6-\frac{33}{2}
  • B 186−31218\sqrt6-\frac{31}{2}
  • C 126−33212\sqrt6-\frac{33}{2}
  • D 126−31212\sqrt6-\frac{31}{2}

Step-by-Step Verified Solution

amp;f(x)=8x3−36x+8amp;=4(2x3−9x+2)amp;=4(x−2)(2x2+4x−1)amp;=4(x−2)(x−−2+62)(x−−262)\begin{aligned}& f(x)=8 x^3-36 x+8 \\\\& =4\left(2 x^3-9 x+2\right) \\\\& =4(x-2)\left(2 x^2+4 x-1\right) \\\\& =4(x-2)\left(x-\frac{-2+\sqrt{6}}{2}\right)\left(x-\frac{-2 \sqrt{6}}{2}\right)\end{aligned}

Local maxima occurs at x=−2+62=x0x=\frac{-2+\sqrt{6}}{2}=x_0

f(x0)=126−332f\left(x_0\right)=12 \sqrt{6}-\frac{33}{2}

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