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Popular >

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

Solution

extreme points

f (x) = \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

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f (x) = 2 x^{3}

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

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

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

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

extreme f(x)=x^5-5x extreme points

f (x) = x^{5} - 5 x

Frequently Asked Questions (FAQ)

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