What is the extreme f(t)=2t+3e^{-kt} ?

The extreme f(t)=2t+3e^{-kt} is Saddle(0, 2/3)

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extreme f(t)=2t+3e^{-kt}

extreme points

f (t) = 2 t + 3 e^{- k t}

Saddle (0, \frac{2}{3})

Solution steps

Find the critical points:

(0, \frac{2}{3})

\frac{\partial ^{2} f}{\partial t ^{2}} = 3 e^{- t k} t^{2}

D (t, k) = 18 e^{- 2 t k} t k - 9 e^{- 2 t k}

Check the sign of at each critical point

Check critical point

(0, \frac{2}{3}) :

Saddle

Saddle (0, \frac{2}{3})

What is the extreme f(t)=2t+3e^{-kt} ?
The extreme f(t)=2t+3e^{-kt} is Saddle(0, 2/3)