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Popular >

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

Solution

extreme points

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

Solution

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

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = 1

into

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

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

Popular Examples

extreme y=x^2-4x+19 extreme points

y = x^{2} - 4 x + 19

extreme f(x)=-6e^{-x^2}extreme points

f (x) = - 6 e^{- x^{2}}

extreme-16x+56y-x^2+4xy-6y^2+6 extreme points

- 16 x + 56 y - x^{2} + 4 x y - 6 y^{2} + 6

extreme y=x^2+10x+21 extreme points

y = x^{2} + 10 x + 21

extreme f(x)=189x-(x^2)/(354)extreme points

f (x) = 189 x - \frac{x ^{2}}{354}

Frequently Asked Questions (FAQ)

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