What is the extreme f(x)=e^{3x}(7-x) ?

The extreme f(x)=e^{3x}(7-x) is Maximum(20/3 ,(e^{20})/3)

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extreme f(x)=e^{3x}(7-x)

extreme points

f (x) = e^{3 x} (7 - x)

Maximum (\frac{20}{3}, \frac{e ^{20}}{3})

Solution steps

f^{'} (x) = e^{3 x} (- 3 x + 20)

Find intervals:

Increasing

: - \infty < x < \frac{20}{3},

Decreasing

: \frac{20}{3} < x < \infty

Plug

x = \frac{20}{3}

into

e^{3 x} (7 - x) : \frac{e ^{20}}{3}

Maximum (\frac{20}{3}, \frac{e ^{20}}{3})

\frac{( - x ^{2} - 8 x + 20 )}{( x ^{2} - 5 x ) ^{2}}

f (x) = 2 x^{2} + 1

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

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

f (x) = - \frac{3 x}{x ^{2} + 1}

What is the extreme f(x)=e^{3x}(7-x) ?
The extreme f(x)=e^{3x}(7-x) is Maximum(20/3 ,(e^{20})/3)