What is the extreme f(x)=3x(x-5)^2 ?

The extreme f(x)=3x(x-5)^2 is Maximum(5/3 , 500/9),Minimum(5,0)

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extreme f(x)=3x(x-5)^2

extreme points

f (x) = 3 x (x - 5)^{2}

Maximum (\frac{5}{3}, \frac{500}{9}), Minimum (5, 0)

Solution steps

f^{'} (x) = 3 (3 x^{2} - 20 x + 25)

Find intervals:

Increasing

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

Decreasing

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

Increasing

: 5 < x < \infty

Plug

x = \frac{5}{3}

into

3 x (x - 5)^{2} : \frac{500}{9}

Maximum (\frac{5}{3}, \frac{500}{9})

Plug

x = 5

into

3 x (x - 5)^{2} : 0

Minimum (5, 0)

Maximum (\frac{5}{3}, \frac{500}{9}), Minimum (5, 0)

What is the extreme f(x)=3x(x-5)^2 ?
The extreme f(x)=3x(x-5)^2 is Maximum(5/3 , 500/9),Minimum(5,0)