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

The extreme f(x)=x^5-5x^4+5x^3-10 is Saddle(0,-10),Maximum(1,-9),Minimum(3,-37)

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

extreme points

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

Saddle (0, - 10), Maximum (1, - 9), Minimum (3, - 37)

Solution steps

f^{'} (x) = 5 x^{4} - 20 x^{3} + 15 x^{2}

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 0

into

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

Saddle (0, - 10)

Plug

x = 1

into

x^{5} - 5 x^{4} + 5 x^{3} - 10 : - 9

Maximum (1, - 9)

Plug

x = 3

into

x^{5} - 5 x^{4} + 5 x^{3} - 10 : - 37

Minimum (3, - 37)

Saddle (0, - 10), Maximum (1, - 9), Minimum (3, - 37)

f (x) = 8 x - 8 ln (x^{2}), (0, + \infty)

f (x, y) = 7 x^{2} y - 8 x y^{3} + 9 y^{3}

\frac{8 - x ^{3}}{x ^{2}}

f (x) = x^{2} lo g_{4} (x)

f (x) = \frac{2 - x ^{2}}{2 x + 1} + 7

What is the extreme f(x)=x^5-5x^4+5x^3-10 ?
The extreme f(x)=x^5-5x^4+5x^3-10 is Saddle(0,-10),Maximum(1,-9),Minimum(3,-37)