What is the extreme f(x)=(-1)/(5x^2+25x+30) ?

The extreme f(x)=(-1)/(5x^2+25x+30) is Minimum(-5/2 , 4/5)

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extreme f(x)=(-1)/(5x^2+25x+30)

extreme

Minimum (- \frac{5}{2}, \frac{4}{5})

Solution steps

f^{'} (x) = \frac{2 x + 5}{5 ( x + 2 ) ^{2} ( x + 3 ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < - \frac{5}{2},

Increasing

: - \frac{5}{2} < x < - 2,

Increasing

: - 2 < x < \infty

Plug

x = - \frac{5}{2}

into

\frac{- 1}{5 x ^{2} + 25 x + 30} : \frac{4}{5}

Minimum (- \frac{5}{2}, \frac{4}{5})

What is the extreme f(x)=(-1)/(5x^2+25x+30) ?
The extreme f(x)=(-1)/(5x^2+25x+30) is Minimum(-5/2 , 4/5)