What is the extreme f(t)=tu(t-2) ?

The extreme f(t)=tu(t-2) is Saddle(0,0),Saddle(2,0)

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extreme f(t)=tu(t-2)

extreme

Saddle (0, 0), Saddle (2, 0)

Solution steps

Find the critical points:

(0, 0), (2, 0)

\frac{\partial ^{2} f}{\partial t ^{2}} = 0

D (t, u) = - 4 t^{2} + 8 t - 4

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(2, 0) :

Saddle

Saddle (0, 0), Saddle (2, 0)

What is the extreme f(t)=tu(t-2) ?
The extreme f(t)=tu(t-2) is Saddle(0,0),Saddle(2,0)