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Popular >

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

Solution

extreme points

\frac{x}{( x + 1 ) ^{2}}

Solution

Maximum (1, \frac{1}{4})

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = 1

into

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

Maximum (1, \frac{1}{4})

Popular Examples

extreme f(x)=-x^4+8x^3-18x^2 extreme points

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

extreme-4x^2+2y^2-2xy extreme points

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

extreme f(x,y)=-2x^2-y^2+xy+8x+3y extreme points

f (x, y) = - 2 x^{2} - y^{2} + x y + 8 x + 3 y

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

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

extreme f(x)=x^3-12x^2+45x+3 extreme points

f (x) = x^{3} - 12 x^{2} + 45 x + 3

Frequently Asked Questions (FAQ)

What is the extreme x/((x+1)^2) ?
The extreme x/((x+1)^2) is Maximum(1, 1/4)