What is the extreme f(t)=10e^{at} ?

The extreme f(t)=10e^{at} is Saddle(0,0)

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extreme f(t)=10e^{at}

extreme points

f (t) = 10 e^{a t}

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial t ^{2}} = 10 e^{t a} t^{2}

D (t, a) = - 200 e^{2 t a} t a - 100 e^{2 t a}

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

f (x) = 2 x^{3} - 6 x^{2} - 90 x + 1

f (x) = (11 - x) (x + 1)^{2}

f (x, y) = 400 - 16 x^{2} - 49 y^{2}

f (x) = 4 x^{3} + 9 x^{2} - 12 x + 5

f (x) = x^{3} - 27 x + 5