What is the extreme (sqrt(x^2+1))/(sqrt(1-x)) ?

The extreme (sqrt(x^2+1))/(sqrt(1-x)) is Minimum(1-sqrt(2),(sqrt(4-2\sqrt{2)})/(\sqrt[4]{2)})

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extreme (sqrt(x^2+1))/(sqrt(1-x))

extreme points

\frac{x ^{2} + 1}{1 - x}

Minimum (1 - 2, \frac{4 - 2 2}{4 2})

Solution steps

f^{'} (x) = \frac{2 x - x ^{2} + 1}{2 x ^{2} + 1 ( - x + 1 ) ^{\frac{3}{2}}}

Find intervals:

Decreasing

: - \infty < x < 1 - 2,

Increasing

: 1 - 2 < x < 1

Plug

x = 1 - 2

into

\frac{x ^{2} + 1}{1 - x} : \frac{4 - 2 2}{4 2}

Minimum (1 - 2, \frac{4 - 2 2}{4 2})

f (x) = 6 x^{3} - 9 x^{2} - 216 x + 3

f (x, y) = 338 y^{2} + x^{2} - x^{2} y

f (x) = - 5 x^{3} + 15 x + 2

f (x) = - x^{2} + 6, - 3 \leq x \leq 4

f (x) = \frac{x + 4}{x ^{2} + 4}

What is the extreme (sqrt(x^2+1))/(sqrt(1-x)) ?
The extreme (sqrt(x^2+1))/(sqrt(1-x)) is Minimum(1-sqrt(2),(sqrt(4-2\sqrt{2)})/(\sqrt[4]{2)})