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

The extreme f(x)=(x+5)e^{-2x} is Maximum(-9/2 ,(e^9)/2)

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

extreme points

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

Maximum (- \frac{9}{2}, \frac{e ^{9}}{2})

Solution steps

f^{'} (x) = - e^{- 2 x} (2 x + 9)

Find intervals:

Increasing

: - \infty < x < - \frac{9}{2},

Decreasing

: - \frac{9}{2} < x < \infty

Plug

x = - \frac{9}{2}

into

(x + 5) e^{- 2 x} : \frac{e ^{9}}{2}

Maximum (- \frac{9}{2}, \frac{e ^{9}}{2})

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

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

f (x) = x^{4} + 32 x^{2}

f (x) = \frac{x ^{4} - 32 x ^{2}}{9}

f (x, y) = x^{3} - 3 x + x y^{2}

What is the extreme f(x)=(x+5)e^{-2x} ?
The extreme f(x)=(x+5)e^{-2x} is Maximum(-9/2 ,(e^9)/2)