What is the extreme C(t)=6.5(e^{-at}-e^{-bt}) ?

The extreme C(t)=6.5(e^{-at}-e^{-bt}) is Saddle(0,b)

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extreme C(t)=6.5(e^{-at}-e^{-bt})

extreme

Saddle (0, b)

Solution steps

Find the critical points:

(0, b)

\frac{\partial ^{2} f}{\partial t ^{2}} = 6.5 e^{- t a} t^{2}

D (t, a) = - 42.25 b^{2} e^{- b t - t a} t^{2} + 84.5 e^{- 2 t a} t a - 42.25 e^{- 2 t a}

Check the sign of at each critical point

Check critical point

(0, b) :

Saddle

Saddle (0, b)

What is the extreme C(t)=6.5(e^{-at}-e^{-bt}) ?
The extreme C(t)=6.5(e^{-at}-e^{-bt}) is Saddle(0,b)