What is the extreme f(x)=6x^5-15x^4+10x^3 ?

The extreme f(x)=6x^5-15x^4+10x^3 is Saddle(0,0),Saddle(1,1)

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extreme f(x)=6x^5-15x^4+10x^3

extreme points

f (x) = 6 x^{5} - 15 x^{4} + 10 x^{3}

Saddle (0, 0), Saddle (1, 1)

Solution steps

Find the critical points:

x = 0, x = 1

Domain of

6 x^{5} - 15 x^{4} + 10 x^{3} : - \infty < x < \infty

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug the extreme point

x = 0

into

6 x^{5} - 15 x^{4} + 10 x^{3} \Rightarrow y = 0

Saddle (0, 0)

Plug the extreme point

x = 1

into

6 x^{5} - 15 x^{4} + 10 x^{3} \Rightarrow y = 1

Saddle (1, 1)

Saddle (0, 0), Saddle (1, 1)

f (x) = 8

f (x) = 6 x^{4} - 8 x^{3} - 24 x^{2} + 1

f (x, y) = y + x e^{y}

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

2 x^{3} - 3 x y + 3 y^{3}

What is the extreme f(x)=6x^5-15x^4+10x^3 ?
The extreme f(x)=6x^5-15x^4+10x^3 is Saddle(0,0),Saddle(1,1)