What is the extreme F(t)=e^{at} ?

The extreme F(t)=e^{at} is Saddle(0,0)

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extreme F(t)=e^{at}

extreme points

F (t) = e^{a t}

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

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

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

f (x) = e^{- a x}

f (x) = - x^{3} + 6 x^{2} - 9 x

f (x) = x^{2} + 9 x + 5

f (x) = x^{4} - 8 x^{2} + a

7 \cdot 8^{x + 8} + 6