What is the extreme f(x)=x^2(180-2x) ?

The extreme f(x)=x^2(180-2x) is Minimum(0,0),Maximum(60,216000)

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extreme f(x)=x^2(180-2x)

extreme

Minimum (0, 0), Maximum (60, 216000)

Solution steps

f^{'} (x) = - 6 x (x - 60)

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 60,

Decreasing

: 60 < x < \infty

Plug

x = 0

into

x^{2} (180 - 2 x) : 0

Minimum (0, 0)

Plug

x = 60

into

x^{2} (180 - 2 x) : 216000

Maximum (60, 216000)

Minimum (0, 0), Maximum (60, 216000)

What is the extreme f(x)=x^2(180-2x) ?
The extreme f(x)=x^2(180-2x) is Minimum(0,0),Maximum(60,216000)