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

The extreme f(x)=x^4-4x^3+10 is Saddle(0,10),Minimum(3,-17)

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

extreme points

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

Saddle (0, 10), Minimum (3, - 17)

Solution steps

f^{'} (x) = 4 x^{3} - 12 x^{2}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 0

into

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

Saddle (0, 10)

Plug

x = 3

into

x^{4} - 4 x^{3} + 10 : - 17

Minimum (3, - 17)

Saddle (0, 10), Minimum (3, - 17)

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

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

\frac{6}{x - 5}

g (x) = \frac{5}{2} x + 4

f (x) = \frac{x - 6}{x + 3}

What is the extreme f(x)=x^4-4x^3+10 ?
The extreme f(x)=x^4-4x^3+10 is Saddle(0,10),Minimum(3,-17)