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

The extreme f(x)=x^3(x-5)^2 is Saddle(0,0),Maximum(3,108),Minimum(5,0)

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

extreme points

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

Saddle (0, 0), Maximum (3, 108), Minimum (5, 0)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < 3,

Decreasing

: 3 < x < 5,

Increasing

: 5 < x < \infty

Plug

x = 0

into

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

Saddle (0, 0)

Plug

x = 3

into

x^{3} (x - 5)^{2} : 108

Maximum (3, 108)

Plug

x = 5

into

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

Minimum (5, 0)

Saddle (0, 0), Maximum (3, 108), Minimum (5, 0)

What is the extreme f(x)=x^3(x-5)^2 ?
The extreme f(x)=x^3(x-5)^2 is Saddle(0,0),Maximum(3,108),Minimum(5,0)