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Popular >

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

Solution

extreme points

y = \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

range of f(x)=1+(8+x)^{1/2}range

f (x) = 1 + (8 + x)^{\frac{1}{2}}

extreme f(x)=3x+9/x extreme points

f (x) = 3 x + \frac{9}{x}

extreme f(x)=xsqrt(16-x^2)extreme points

f (x) = x 16 - x^{2}

inverse of f(x)=sqrt(x+6)inverse

f (x) = x + 6

slope of-3x+2y=20 slope

- 3 x + 2 y = 20

Frequently Asked Questions (FAQ)

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