What is the extreme y=9e^{-2t}-7e^{-3t} ?

The extreme y=9e^{-2t}-7e^{-3t} is Maximum(ln(7/6), 108/49)

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extreme y=9e^{-2t}-7e^{-3t}

extreme points

y = 9 e^{- 2 t} - 7 e^{- 3 t}

Maximum (ln (\frac{7}{6}), \frac{108}{49})

Solution steps

f^{'} (t) = 3 e^{- 3 t} (- 6 e^{t} + 7)

Find intervals:

Increasing

: - \infty < t < ln (\frac{7}{6}),

Decreasing

: ln (\frac{7}{6}) < t < \infty

Plug

t = ln (\frac{7}{6})

into

9 e^{- 2 t} - 7 e^{- 3 t} : \frac{108}{49}

Maximum (ln (\frac{7}{6}), \frac{108}{49})

18 x - 8

x^{6} - x^{4} + 4 x^{3} - 2 x

f (x) = (x^{2} - 4)^{4} (x^{2} + 1)^{5}

\frac{2 x - ln ( 3 x )}{x}

f (x) = 3 x^{4} - 54 x^{2} + 2

What is the extreme y=9e^{-2t}-7e^{-3t} ?
The extreme y=9e^{-2t}-7e^{-3t} is Maximum(ln(7/6), 108/49)