What is the extreme f(x)=e^{3x}(3-x) ?

The extreme f(x)=e^{3x}(3-x) is Maximum(8/3 ,(e^8)/3)

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extreme f(x)=e^{3x}(3-x)

extreme

Maximum (\frac{8}{3}, \frac{e ^{8}}{3})

Solution steps

f^{'} (x) = e^{3 x} (- 3 x + 8)

Find intervals:

Increasing

: - \infty < x < \frac{8}{3},

Decreasing

: \frac{8}{3} < x < \infty

Plug

x = \frac{8}{3}

into

e^{3 x} (3 - x) : \frac{e ^{8}}{3}

Maximum (\frac{8}{3}, \frac{e ^{8}}{3})

What is the extreme f(x)=e^{3x}(3-x) ?
The extreme f(x)=e^{3x}(3-x) is Maximum(8/3 ,(e^8)/3)