What is the extreme f(x)=x^2(6-x)^3 ?

The extreme f(x)=x^2(6-x)^3 is Minimum(0,0),Maximum(12/5 , 839808/3125),Saddle(6,0)

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

extreme

Minimum (0, 0), Maximum (\frac{12}{5}, \frac{839808}{3125}), Saddle (6, 0)

Solution steps

f^{'} (x) = - x (x - 6)^{2} (5 x - 12)

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{12}{5},

Decreasing

: \frac{12}{5} < x < 6,

Decreasing

: 6 < x < \infty

Plug

x = 0

into

x^{2} (6 - x)^{3} : 0

Minimum (0, 0)

Plug

x = \frac{12}{5}

into

x^{2} (6 - x)^{3} : \frac{839808}{3125}

Maximum (\frac{12}{5}, \frac{839808}{3125})

Plug

x = 6

into

x^{2} (6 - x)^{3} : 0

Saddle (6, 0)

Minimum (0, 0), Maximum (\frac{12}{5}, \frac{839808}{3125}), Saddle (6, 0)

What is the extreme f(x)=x^2(6-x)^3 ?
The extreme f(x)=x^2(6-x)^3 is Minimum(0,0),Maximum(12/5 , 839808/3125),Saddle(6,0)