What is the extreme x/(x^2+6x+5) ?

The extreme x/(x^2+6x+5) is Minimum(-sqrt(5),(3+sqrt(5))/8),Maximum(sqrt(5),(3-sqrt(5))/8)

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extreme x/(x^2+6x+5)

extreme points

\frac{x}{x ^{2} + 6 x + 5}

Minimum (- 5, \frac{3 + 5}{8}), Maximum (5, \frac{3 - 5}{8})

Solution steps

f^{'} (x) = \frac{- x ^{2} + 5}{( x ^{2} + 6 x + 5 ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < - 5,

Decreasing

: - 5 < x < - 5,

Increasing

: - 5 < x < - 1,

Increasing

: - 1 < x < 5,

Decreasing

: 5 < x < \infty

Plug

x = - 5

into

\frac{x}{x ^{2} + 6 x + 5} : \frac{3 + 5}{8}

Minimum (- 5, \frac{3 + 5}{8})

Plug

x = 5

into

\frac{x}{x ^{2} + 6 x + 5} : \frac{3 - 5}{8}

Maximum (5, \frac{3 - 5}{8})

Minimum (- 5, \frac{3 + 5}{8}), Maximum (5, \frac{3 - 5}{8})

f (x) = 2 - 2 x

f (x) = - 3^{x}

f (x) = c^{x}

1 0^{x}

What is the extreme x/(x^2+6x+5) ?
The extreme x/(x^2+6x+5) is Minimum(-sqrt(5),(3+sqrt(5))/8),Maximum(sqrt(5),(3-sqrt(5))/8)