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Popular >

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

Solution

extreme points

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

Solution

Minimum (- 1, - \frac{1}{2}), Maximum (1, \frac{1}{2})

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

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

Minimum (- 1, - \frac{1}{2})

Plug

x = 1

into

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

Maximum (1, \frac{1}{2})

Minimum (- 1, - \frac{1}{2}), Maximum (1, \frac{1}{2})

Popular Examples

extreme f(x)=x^3-3x^2+3x-1 extreme points

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

extreme f(x)=4x^5-7x^2+8 extreme points

f (x) = 4 x^{5} - 7 x^{2} + 8

extreme f(x)= x/(x^2+1),(-1,2)extreme points

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

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

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

extreme f(x)=9x^2-4x extreme points

f (x) = 9 x^{2} - 4 x

Frequently Asked Questions (FAQ)

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