What is the extreme f(x)=(x-9)^3(x+5)^2 ?

The extreme f(x)=(x-9)^3(x+5)^2 is Maximum(-5,0),Minimum(3/5 ,-58084992/3125),Saddle(9,0)

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extreme f(x)=(x-9)^3(x+5)^2

extreme

Maximum (- 5, 0), Minimum (\frac{3}{5}, - \frac{58084992}{3125}), Saddle (9, 0)

Solution steps

f^{'} (x) = (x - 9)^{2} (x + 5) (5 x - 3)

Find intervals:

Increasing

: - \infty < x < - 5,

Decreasing

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

Increasing

: \frac{3}{5} < x < 9,

Increasing

: 9 < x < \infty

Plug

x = - 5

into

(x - 9)^{3} (x + 5)^{2} : 0

Maximum (- 5, 0)

Plug

x = \frac{3}{5}

into

(x - 9)^{3} (x + 5)^{2} : - \frac{58084992}{3125}

Minimum (\frac{3}{5}, - \frac{58084992}{3125})

Plug

x = 9

into

(x - 9)^{3} (x + 5)^{2} : 0

Saddle (9, 0)

Maximum (- 5, 0), Minimum (\frac{3}{5}, - \frac{58084992}{3125}), Saddle (9, 0)

What is the extreme f(x)=(x-9)^3(x+5)^2 ?
The extreme f(x)=(x-9)^3(x+5)^2 is Maximum(-5,0),Minimum(3/5 ,-58084992/3125),Saddle(9,0)