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

The extreme x^2(2-x)^3 is Minimum(0,0),Maximum(4/5 , 3456/3125),Saddle(2,0)

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extreme x^2(2-x)^3

extreme

Minimum (0, 0), Maximum (\frac{4}{5}, \frac{3456}{3125}), Saddle (2, 0)

Solution steps

f^{'} (x) = - x (x - 2)^{2} (5 x - 4)

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{4}{5},

Decreasing

: \frac{4}{5} < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = 0

into

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

Minimum (0, 0)

Plug

x = \frac{4}{5}

into

x^{2} (2 - x)^{3} : \frac{3456}{3125}

Maximum (\frac{4}{5}, \frac{3456}{3125})

Plug

x = 2

into

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

Saddle (2, 0)

Minimum (0, 0), Maximum (\frac{4}{5}, \frac{3456}{3125}), Saddle (2, 0)

What is the extreme x^2(2-x)^3 ?
The extreme x^2(2-x)^3 is Minimum(0,0),Maximum(4/5 , 3456/3125),Saddle(2,0)