What is the extreme f(x)=x^4-8x^3+7 ?

The extreme f(x)=x^4-8x^3+7 is Saddle(0,7),Minimum(6,-425)

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extreme f(x)=x^4-8x^3+7

extreme points

f (x) = x^{4} - 8 x^{3} + 7

Saddle (0, 7), Minimum (6, - 425)

Solution steps

f^{'} (x) = 4 x^{3} - 24 x^{2}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 6,

Increasing

: 6 < x < \infty

Plug

x = 0

into

x^{4} - 8 x^{3} + 7 : 7

Saddle (0, 7)

Plug

x = 6

into

x^{4} - 8 x^{3} + 7 : - 425

Minimum (6, - 425)

Saddle (0, 7), Minimum (6, - 425)

What is the extreme f(x)=x^4-8x^3+7 ?
The extreme f(x)=x^4-8x^3+7 is Saddle(0,7),Minimum(6,-425)