What is the extreme f(x)=1-e^{-ax} ?

The extreme f(x)=1-e^{-ax} is Saddle(0,0)

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extreme f(x)=1-e^{-ax}

extreme points

f (x) = 1 - 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)