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Popular >

extreme f(x)=(x^2)/((x^2-1))

Solution

extreme points

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

Solution

Maximum (0, 0)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = 0

into

\frac{x ^{2}}{x ^{2} - 1} : 0

Maximum (0, 0)

Popular Examples

extreme f(x)=3x^2-4x+5 extreme points

f (x) = 3 x^{2} - 4 x + 5

extreme f(x)=2x-3x^{2/3},-1<= x<= 3 extreme points

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

extreme x(1-x^2)^2 extreme points

x (1 - x^{2})^{2}

extreme f(x,y)=x^2+xy+y^2-10y+33 extreme points

f (x, y) = x^{2} + x y + y^{2} - 10 y + 33

extreme y=x^2+4x extreme points

y = x^{2} + 4 x

Frequently Asked Questions (FAQ)

What is the extreme f(x)=(x^2)/((x^2-1)) ?
The extreme f(x)=(x^2)/((x^2-1)) is Maximum(0,0)