What is the extreme f(x)=(x-1)^2+sqrt(4-4x^2) ?

The extreme f(x)=(x-1)^2+sqrt(4-4x^2) is Minimum(-1,4),Maximum(-0.88320…,4.48443…),Minimum(1,0)

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extreme f(x)=(x-1)^2+sqrt(4-4x^2)

extreme points

f (x) = (x - 1)^{2} + 4 - 4 x^{2}

Minimum (- 1, 4), Maximum (- 0.88320 \dots, 4.48443 \dots), Minimum (1, 0)

Solution steps

Find the critical points:

x = - 1, x \approx - 0.88320 \dots, x = 1

Domain of

(x - 1)^{2} + 4 - 4 x^{2} : - 1 \leq x \leq 1

Find intervals:

Increasing

: - 1 < x < - 0.88320 \dots,

Decreasing

: - 0.88320 \dots < x < 1

Plug the extreme point

x = - 1

into

(x - 1)^{2} + 4 - 4 x^{2} \Rightarrow y = 4

Minimum (- 1, 4)

Plug the extreme point

x = - 0.88320 \dots

into

(x - 1)^{2} + 4 - 4 x^{2} \Rightarrow y = 4.48443 \dots

Maximum (- 0.88320 \dots, 4.48443 \dots)

Plug the extreme point

x = 1

into

(x - 1)^{2} + 4 - 4 x^{2} \Rightarrow y = 0

Minimum (1, 0)

Minimum (- 1, 4), Maximum (- 0.88320 \dots, 4.48443 \dots), Minimum (1, 0)

x^{2} - 5 x y + 4 y^{2} - 2 x + 5 y

f (x) = x^{2} + 4 x + 11

f (x) = x^{2} + 4 x + 10

f (x) = x^{2} + 4 x + 17

f (x) = x 324 - x^{2}

What is the extreme f(x)=(x-1)^2+sqrt(4-4x^2) ?
The extreme f(x)=(x-1)^2+sqrt(4-4x^2) is Minimum(-1,4),Maximum(-0.88320…,4.48443…),Minimum(1,0)