Let x = 2 be a local minima of the function f ( x ) = 2 x 4 - 18 x 2 + 8 x + 12 , x ( - 4 , 4 ) . If M is the local maximum value of the function f in (- 4, 4), then M = [2023]

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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 the local maximum value of the function $f$ in (- 4, 4), then $M =$ [2023]

1 $18 \sqrt{6} - \frac{33}{2}$

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

3 $12 \sqrt{6} - \frac{31}{2}$

4 $18 \sqrt{6} - \frac{31}{2}$

Ans.
(2)

$f (x) = 2 x^{4} - 18 x^{2} + 8 x + 12$

$f' (x) = 8 x^{3} - 36 x + 8 = 4 (x - 2) (2 x^{2} + 4 x - 1)$

Sign of $f' (x)$ is given below

Point of maxima = $\frac{\sqrt{6} - 2}{2}$

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

Solution

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 the local maximum value of the function $f$ in (- 4, 4), then $M =$ [2023]

1 $18 \sqrt{6} - \frac{33}{2}$

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

3 $12 \sqrt{6} - \frac{31}{2}$

4 $18 \sqrt{6} - \frac{31}{2}$

Ans.
(2)

$f (x) = 2 x^{4} - 18 x^{2} + 8 x + 12$

$f' (x) = 8 x^{3} - 36 x + 8 = 4 (x - 2) (2 x^{2} + 4 x - 1)$

Sign of $f' (x)$ is given below

Point of maxima = $\frac{\sqrt{6} - 2}{2}$

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

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Solution

Q. Let x = 2 be a local minima of the function f(x)=2x4-18x2+8x+12, x∈(-4,4). If M is the local maximum value of the function f in (- 4, 4), then M= [2023]

1 186-332

2 126-332

3 126-312

4 186-312

Ans. (2) f(x)=2x4-18x2+8x+12 f'(x)=8x3-36x+8=4(x-2)(2x2+4x-1) Sign of f'(x) is given below Point of maxima = 6-22 M=126-332

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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 the local maximum value of the function $f$ in (- 4, 4), then $M =$ [2023]

1 $18 \sqrt{6} - \frac{33}{2}$

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

3 $12 \sqrt{6} - \frac{31}{2}$

4 $18 \sqrt{6} - \frac{31}{2}$

Ans.
(2)

$f (x) = 2 x^{4} - 18 x^{2} + 8 x + 12$

$f' (x) = 8 x^{3} - 36 x + 8 = 4 (x - 2) (2 x^{2} + 4 x - 1)$

Sign of $f' (x)$ is given below

Point of maxima = $\frac{\sqrt{6} - 2}{2}$

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