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)

x 8 - x^{2}

f (x) = \frac{( x + 4 ) ( x + 1 ) ( x - 1 ) ( x - 3 )}{x}

f (x) = 2 x^{3} - 12 x^{2} + 8

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

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