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

The extreme f(x)=x(x-10)^2 is Maximum(10/3 , 4000/27),Minimum(10,0)

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

extreme points

f (x) = x (x - 10)^{2}

Maximum (\frac{10}{3}, \frac{4000}{27}), Minimum (10, 0)

Solution steps

f^{'} (x) = (x - 10) (3 x - 10)

Find intervals:

Increasing

: - \infty < x < \frac{10}{3},

Decreasing

: \frac{10}{3} < x < 10,

Increasing

: 10 < x < \infty

Plug

x = \frac{10}{3}

into

x (x - 10)^{2} : \frac{4000}{27}

Maximum (\frac{10}{3}, \frac{4000}{27})

Plug

x = 10

into

x (x - 10)^{2} : 0

Minimum (10, 0)

Maximum (\frac{10}{3}, \frac{4000}{27}), Minimum (10, 0)

5 x^{4} - x^{5} + 4

f (x) = x^{2} + 2 y + y^{2} - 8

f (x) = x 3 x - x^{2}

y = cos (3 x) - 2

f (x) = - 3 x^{3} + 4 x^{2}, - 2 \leq x \leq 2

What is the extreme f(x)=x(x-10)^2 ?
The extreme f(x)=x(x-10)^2 is Maximum(10/3 , 4000/27),Minimum(10,0)