What is the extreme f(x)=x^5-10x^4+25x^3 ?

The extreme f(x)=x^5-10x^4+25x^3 is Saddle(0,0),Maximum(3,108),Minimum(5,0)

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extreme f(x)=x^5-10x^4+25x^3

extreme points

f (x) = x^{5} - 10 x^{4} + 25 x^{3}

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

Solution steps

f^{'} (x) = 5 x^{4} - 40 x^{3} + 75 x^{2}

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < 3,

Decreasing

: 3 < x < 5,

Increasing

: 5 < x < \infty

Plug

x = 0

into

x^{5} - 10 x^{4} + 25 x^{3} : 0

Saddle (0, 0)

Plug

x = 3

into

x^{5} - 10 x^{4} + 25 x^{3} : 108

Maximum (3, 108)

Plug

x = 5

into

x^{5} - 10 x^{4} + 25 x^{3} : 0

Minimum (5, 0)

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

1 + 6 x^{2} - x^{3}

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

f (x) = x^{4} - 8 x^{3} + 5

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

f (x) = 4 x - 8 x

What is the extreme f(x)=x^5-10x^4+25x^3 ?
The extreme f(x)=x^5-10x^4+25x^3 is Saddle(0,0),Maximum(3,108),Minimum(5,0)