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Popular Functions >

extreme y= x/(x^2+4)

Solution

extreme

Solution

Minimum (- 2, - \frac{1}{4}), Maximum (2, \frac{1}{4})

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - 2

into

\frac{x}{x ^{2} + 4} : - \frac{1}{4}

Minimum (- 2, - \frac{1}{4})

Plug

x = 2

into

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

Maximum (2, \frac{1}{4})

Minimum (- 2, - \frac{1}{4}), Maximum (2, \frac{1}{4})

Graph

Popular Examples

extreme y=x(x-1)^5

extreme f(x)=x^3+6x^2-6

extreme f(x,y)=xy+x^2+y^2-x+y+17

extreme f(x)=2x^3-3x^2-12x+1,-4<= x<= 5

extreme f(x)=sqrt(3)x+2cos(x)

Frequently Asked Questions (FAQ)

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