What is the extreme f(x)=3x^4-8x^3+10 ?

The extreme f(x)=3x^4-8x^3+10 is Saddle(0,10),Minimum(2,-6)

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extreme f(x)=3x^4-8x^3+10

extreme

Saddle (0, 10), Minimum (2, - 6)

Solution steps

f^{'} (x) = 12 x^{3} - 24 x^{2}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = 0

into

3 x^{4} - 8 x^{3} + 10 : 10

Saddle (0, 10)

Plug

x = 2

into

3 x^{4} - 8 x^{3} + 10 : - 6

Minimum (2, - 6)

Saddle (0, 10), Minimum (2, - 6)

What is the extreme f(x)=3x^4-8x^3+10 ?
The extreme f(x)=3x^4-8x^3+10 is Saddle(0,10),Minimum(2,-6)