What is the extreme f(t)=e^{kt} ?

The extreme f(t)=e^{kt} is Saddle(0,0)

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extreme f(t)=e^{kt}

extreme points

f (t) = e^{k t}

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial t ^{2}} = e^{t k} t^{2}

D (t, k) = - 2 e^{2 t k} t k - e^{2 t k}

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)