What is the extreme f(x)=5e^x-e^{2x} ?

The extreme f(x)=5e^x-e^{2x} is Maximum(ln(5)-ln(2), 25/2-e^{2(ln(5)-ln(2))})

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extreme f(x)=5e^x-e^{2x}

extreme

Maximum (ln (5) - ln (2), \frac{25}{2} - e^{2 (l n (5) - l n (2))})

Solution steps

f^{'} (x) = 5 e^{x} - e^{2 x} \cdot 2

Find intervals:

Increasing

: - \infty < x < ln (\frac{5}{2}),

Decreasing

: ln (\frac{5}{2}) < x < \infty

Plug

x = ln (5) - ln (2)

into

5 e^{x} - e^{2 x} : \frac{25}{2} - e^{2 (l n (5) - l n (2))}

Maximum (ln (5) - ln (2), \frac{25}{2} - e^{2 (l n (5) - l n (2))})

What is the extreme f(x)=5e^x-e^{2x} ?
The extreme f(x)=5e^x-e^{2x} is Maximum(ln(5)-ln(2), 25/2-e^{2(ln(5)-ln(2))})