What is the extreme f(x)=(10-2x)(10-2x)(x) ?

The extreme f(x)=(10-2x)(10-2x)(x) is Maximum(5/3 , 2000/27),Minimum(5,0)

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extreme f(x)=(10-2x)(10-2x)(x)

extreme

Maximum (\frac{5}{3}, \frac{2000}{27}), Minimum (5, 0)

Solution steps

f^{'} (x) = 4 (x - 5) (3 x - 5)

Find intervals:

Increasing

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

Decreasing

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

Increasing

: 5 < x < \infty

Plug

x = \frac{5}{3}

into

(10 - 2 x) (10 - 2 x) x : \frac{2000}{27}

Maximum (\frac{5}{3}, \frac{2000}{27})

Plug

x = 5

into

(10 - 2 x) (10 - 2 x) x : 0

Minimum (5, 0)

Maximum (\frac{5}{3}, \frac{2000}{27}), Minimum (5, 0)

What is the extreme f(x)=(10-2x)(10-2x)(x) ?
The extreme f(x)=(10-2x)(10-2x)(x) is Maximum(5/3 , 2000/27),Minimum(5,0)