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

The extreme (x^2)/(sqrt(x^2-1)) is Minimum(-sqrt(2),2),Minimum(sqrt(2),2)

Popular >

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

extreme points

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

Minimum (- 2, 2), Minimum (2, 2)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < - 1,

Decreasing

: 1 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 2

into

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

Minimum (- 2, 2)

Plug

x = 2

into

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

Minimum (2, 2)

Minimum (- 2, 2), Minimum (2, 2)

f (x) = x^{4} - 8 x^{3} + 16 x^{2} - 10

f (x) = 9 + 18 x - 3 x^{2}

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

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

E (x, y) = 4 x^{2} - 6 x + 9 + y - 8 y^{2} + 5

What is the extreme (x^2)/(sqrt(x^2-1)) ?
The extreme (x^2)/(sqrt(x^2-1)) is Minimum(-sqrt(2),2),Minimum(sqrt(2),2)