What is the extreme 3x^4-7x^2+6x^2-5x-8 ?

The extreme 3x^4-7x^2+6x^2-5x-8 is Minimum(0.82106…,-11.41604…)

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extreme 3x^4-7x^2+6x^2-5x-8

extreme points

3 x^{4} - 7 x^{2} + 6 x^{2} - 5 x - 8

Minimum (0.82106 \dots, - 11.41604 \dots)

Solution steps

Find the critical points:

x \approx 0.82106 \dots

Domain of

3 x^{4} - 7 x^{2} + 6 x^{2} - 5 x - 8 : - \infty < x < \infty

Find intervals:

Decreasing

: - \infty < x < 0.82106 \dots,

Increasing

: 0.82106 \dots < x < \infty

Plug the extreme point

x = 0.82106 \dots

into

3 x^{4} - 7 x^{2} + 6 x^{2} - 5 x - 8 \Rightarrow y = - 11.41604 \dots

Minimum (0.82106 \dots, - 11.41604 \dots)

f (x, y) = 2 + 2 x + 2 y - x^{2} - y^{2}

P (x, y) = 200 x^{\frac{1}{2}} y^{\frac{1}{2}}

f (x) = \frac{x ^{2}}{9 - x ^{2}}

f (x, y) = x^{2} + y^{2} + \frac{2}{x y}

190 + 8 x^{3} + x^{4}

What is the extreme 3x^4-7x^2+6x^2-5x-8 ?
The extreme 3x^4-7x^2+6x^2-5x-8 is Minimum(0.82106…,-11.41604…)