What is the extreme f(x)=(4-x)*e^{2x} ?

The extreme f(x)=(4-x)*e^{2x} is Maximum(7/2 ,(e^7)/2)

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extreme f(x)=(4-x)*e^{2x}

extreme points

f (x) = (4 - x) \cdot e^{2 x}

Maximum (\frac{7}{2}, \frac{e ^{7}}{2})

Solution steps

f^{'} (x) = e^{2 x} (- 2 x + 7)

Find intervals:

Increasing

: - \infty < x < \frac{7}{2},

Decreasing

: \frac{7}{2} < x < \infty

Plug

x = \frac{7}{2}

into

(4 - x) \cdot e^{2 x} : \frac{e ^{7}}{2}

Maximum (\frac{7}{2}, \frac{e ^{7}}{2})

What is the extreme f(x)=(4-x)*e^{2x} ?
The extreme f(x)=(4-x)*e^{2x} is Maximum(7/2 ,(e^7)/2)