What is the extreme f(x)=5x^4-20x^3+1 ?

The extreme f(x)=5x^4-20x^3+1 is Saddle(0,1),Minimum(3,-134)

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extreme f(x)=5x^4-20x^3+1

extreme points

f (x) = 5 x^{4} - 20 x^{3} + 1

Saddle (0, 1), Minimum (3, - 134)

Solution steps

f^{'} (x) = 20 x^{3} - 60 x^{2}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 0

into

5 x^{4} - 20 x^{3} + 1 : 1

Saddle (0, 1)

Plug

x = 3

into

5 x^{4} - 20 x^{3} + 1 : - 134

Minimum (3, - 134)

Saddle (0, 1), Minimum (3, - 134)

f (x) = 0.001 x^{2} + 3.2 x - 10

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

f (x) = - 7 x^{2} - 7 x y - 6 y^{2} - 35 x - 26 y + 9

3 (x - 4)^{\frac{2}{3}} + 6

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

What is the extreme f(x)=5x^4-20x^3+1 ?
The extreme f(x)=5x^4-20x^3+1 is Saddle(0,1),Minimum(3,-134)