What is the extreme f(x)=3x^4-24x^3+25 ?

The extreme f(x)=3x^4-24x^3+25 is Saddle(0,25),Minimum(6,-1271)

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extreme f(x)=3x^4-24x^3+25

extreme points

f (x) = 3 x^{4} - 24 x^{3} + 25

Saddle (0, 25), Minimum (6, - 1271)

Solution steps

f^{'} (x) = 12 x^{3} - 72 x^{2}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 6,

Increasing

: 6 < x < \infty

Plug

x = 0

into

3 x^{4} - 24 x^{3} + 25 : 25

Saddle (0, 25)

Plug

x = 6

into

3 x^{4} - 24 x^{3} + 25 : - 1271

Minimum (6, - 1271)

Saddle (0, 25), Minimum (6, - 1271)

What is the extreme f(x)=3x^4-24x^3+25 ?
The extreme f(x)=3x^4-24x^3+25 is Saddle(0,25),Minimum(6,-1271)