What is the extreme f(x)=g(t)=6t^4-8t^3+5 ?

The extreme f(x)=g(t)=6t^4-8t^3+5 is Saddle(0,5),Minimum(1,3)

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extreme f(x)=g(t)=6t^4-8t^3+5

extreme

Saddle (0, 5), Minimum (1, 3)

Solution steps

f^{'} (t) = 24 t^{3} - 24 t^{2}

Find intervals:

Decreasing

: - \infty < t < 0,

Decreasing

: 0 < t < 1,

Increasing

: 1 < t < \infty

Plug

t = 0

into

6 t^{4} - 8 t^{3} + 5 : 5

Saddle (0, 5)

Plug

t = 1

into

6 t^{4} - 8 t^{3} + 5 : 3

Minimum (1, 3)

Saddle (0, 5), Minimum (1, 3)

What is the extreme f(x)=g(t)=6t^4-8t^3+5 ?
The extreme f(x)=g(t)=6t^4-8t^3+5 is Saddle(0,5),Minimum(1,3)