What is the extreme f(x)=5x^6-6x^5+1 ?

The extreme f(x)=5x^6-6x^5+1 is Saddle(0,1),Minimum(1,0)

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extreme f(x)=5x^6-6x^5+1

extreme points

f (x) = 5 x^{6} - 6 x^{5} + 1

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

Solution steps

f^{'} (x) = 30 x^{5} - 30 x^{4}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = 0

into

5 x^{6} - 6 x^{5} + 1 : 1

Saddle (0, 1)

Plug

x = 1

into

5 x^{6} - 6 x^{5} + 1 : 0

Minimum (1, 0)

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

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

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

f (x) = \frac{2 x}{x ^{2} + 2}

f (x, y) = 400 - 49 x^{2} - 36 y^{2}

f (x) = \frac{3 ( x - 4 ) ^{2}}{x + 1}

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