What is the extreme f(x)=6x^4-8x^3+2 ?

The extreme f(x)=6x^4-8x^3+2 is Saddle(0,2),Minimum(1,0)

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extreme f(x)=6x^4-8x^3+2

extreme

Saddle (0, 2), Minimum (1, 0)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = 0

into

6 x^{4} - 8 x^{3} + 2 : 2

Saddle (0, 2)

Plug

x = 1

into

6 x^{4} - 8 x^{3} + 2 : 0

Minimum (1, 0)

Saddle (0, 2), Minimum (1, 0)

What is the extreme f(x)=6x^4-8x^3+2 ?
The extreme f(x)=6x^4-8x^3+2 is Saddle(0,2),Minimum(1,0)