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

Question

Let x=2 be a local minima of the function f(x)=2 x4-18 x2+8 x+12, x ∈(-4,4). If M is local maximum value of the function f in (-4,4), then M = (A) 18 √6-(33/2) (B) 12 √6-(33/2) (C) 12 √6-(31/2) (D) 18 √6-(31/2)

Tardigrade Admin · Accepted Answer

f prime(x)=8 x3-36 x+8=4(2 x3-9 x+2) f prime(x)=0 ∴ x=(√6-2/2) Now f(x)=(x2-2 x-(9/2))(2 x2+4 x-1)+24 x+7.5 ∴ f((√6-2/2))=M=12 √6-(33/2)

Q. 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 $M =$

$186 - \frac{33}{2}$

$126 - \frac{33}{2}$

$126 - \frac{31}{2}$

$186 - \frac{31}{2}$

$f^{'} (x) = 8 x^{3} - 36 x + 8 = 4 (2 x^{3} - 9 x + 2)$
$f^{'} (x) = 0$
$∴ x = \frac{6 - 2}{2}$
Now
$f (x) = (x^{2} - 2 x - \frac{9}{2}) (2 x^{2} + 4 x - 1) + 24 x + 7.5$
$∴ f (\frac{6 - 2}{2}) = M = 126 - \frac{33}{2}$

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

186​−233​

126​−233​

126​−231​

186​−231​