What is the extreme f(x)=e^{-ax} ?

The extreme f(x)=e^{-ax} is Saddle(0,0)

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extreme f(x)=e^{-ax}

extreme points

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

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = e^{- x a} x^{2}

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

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

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

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