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)

f (x, y) = \frac{( 2 x - x ^{2} ) ( 2 y - y ^{2} )}{x y}

f (x, y) = x^{3} - y^{2} - 12 x + 6 y

f (x) = x^{4} - 8 x^{3} + 4

y = x^{5} - x^{3}

x^{3} + 1