What is the extreme y=-4e^{-4t}+5e^{-5t} ?

The extreme y=-4e^{-4t}+5e^{-5t} is Minimum(ln(25/16),-262144/1953125)

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extreme y=-4e^{-4t}+5e^{-5t}

extreme

Minimum (ln (\frac{25}{16}), - \frac{262144}{1953125})

Solution steps

f^{'} (t) = e^{- 5 t} (16 e^{t} - 25)

Find intervals:

Decreasing

: - \infty < t < ln (\frac{25}{16}),

Increasing

: ln (\frac{25}{16}) < t < \infty

Plug

t = ln (\frac{25}{16})

into

- 4 e^{- 4 t} + 5 e^{- 5 t} : - \frac{262144}{1953125}

Minimum (ln (\frac{25}{16}), - \frac{262144}{1953125})

What is the extreme y=-4e^{-4t}+5e^{-5t} ?
The extreme y=-4e^{-4t}+5e^{-5t} is Minimum(ln(25/16),-262144/1953125)