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 points

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

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))})

f (x, y) = 4 x^{2} + 2 y^{2} + 5

1 - ∣ x ∣

f (x) = - 8 x^{3} + 24 x + 9

f (x) = 5 x^{2} - 4 y^{2} - 7 x + 5 y + 4

(3 x + 2) (2 x + 5)

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))})