What is the extreme f(x)=(120-6w)w^2 ?

The extreme f(x)=(120-6w)w^2 is Minimum(0,0),Maximum(40/3 , 64000/9)

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extreme f(x)=(120-6w)w^2

extreme

Minimum (0, 0), Maximum (\frac{40}{3}, \frac{64000}{9})

Solution steps

f^{'} (w) = 6 w (- 3 w + 40)

Find intervals:

Decreasing

: - \infty < w < 0,

Increasing

: 0 < w < \frac{40}{3},

Decreasing

: \frac{40}{3} < w < \infty

Plug

w = 0

into

(120 - 6 w) w^{2} : 0

Minimum (0, 0)

Plug

w = \frac{40}{3}

into

(120 - 6 w) w^{2} : \frac{64000}{9}

Maximum (\frac{40}{3}, \frac{64000}{9})

Minimum (0, 0), Maximum (\frac{40}{3}, \frac{64000}{9})

What is the extreme f(x)=(120-6w)w^2 ?
The extreme f(x)=(120-6w)w^2 is Minimum(0,0),Maximum(40/3 , 64000/9)