What is the extreme 4x^2+6+6/(x^2-4x+4) ?

The extreme 4x^2+6+6/(x^2-4x+4) is Minimum(-0.15076…,7.38799…),Minimum(2.81109…,46.72929…)

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extreme 4x^2+6+6/(x^2-4x+4)

extreme points

4 x^{2} + 6 + \frac{6}{x ^{2} - 4 x + 4}

Minimum (- 0.15076 \dots, 7.38799 \dots), Minimum (2.81109 \dots, 46.72929 \dots)

Solution steps

Find the critical points:

x \approx - 0.15076 \dots, x \approx 2.81109 \dots

Domain of

4 x^{2} + 6 + \frac{6}{x ^{2} - 4 x + 4} : x < 2 or x > 2

Find intervals:

Decreasing

: - \infty < x < - 0.15076 \dots,

Increasing

: - 0.15076 \dots < x < 2,

Decreasing

: 2 < x < 2.81109 \dots,

Increasing

: 2.81109 \dots < x < \infty

Plug the extreme point

x = - 0.15076 \dots

into

4 x^{2} + 6 + \frac{6}{x ^{2} - 4 x + 4} \Rightarrow y = 7.38799 \dots

Minimum (- 0.15076 \dots, 7.38799 \dots)

Plug the extreme point

x = 2.81109 \dots

into

4 x^{2} + 6 + \frac{6}{x ^{2} - 4 x + 4} \Rightarrow y = 46.72929 \dots

Minimum (2.81109 \dots, 46.72929 \dots)

Minimum (- 0.15076 \dots, 7.38799 \dots), Minimum (2.81109 \dots, 46.72929 \dots)

(x - y) (25 - x y)

f (x, y) = 2 x^{2} + 3 y^{2}

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

f (x) = - x^{4} - 8 x^{3} - 18 x^{2} + 7

f (x, y) = - y^{2} + x y - x^{3} + y + 3

What is the extreme 4x^2+6+6/(x^2-4x+4) ?
The extreme 4x^2+6+6/(x^2-4x+4) is Minimum(-0.15076…,7.38799…),Minimum(2.81109…,46.72929…)