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

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

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

extreme points

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

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

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

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)