What is the extreme f(x)=(x-3)e^{-5x} ?

The extreme f(x)=(x-3)e^{-5x} is Maximum(16/5 , 1/(5e^{16)})

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extreme f(x)=(x-3)e^{-5x}

extreme points

f (x) = (x - 3) e^{- 5 x}

Maximum (\frac{16}{5}, \frac{1}{5 e ^{16}})

Solution steps

f^{'} (x) = - e^{- 5 x} (5 x - 16)

Find intervals:

Increasing

: - \infty < x < \frac{16}{5}

Plug

x = \frac{16}{5}

into

(x - 3) e^{- 5 x} : \frac{1}{5 e ^{16}}

Maximum (\frac{16}{5}, \frac{1}{5 e ^{16}})

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

g (x) = e^{- x^{4}}, - 3 \leq x \leq 1

f (x, y) = x^{2} + y^{2} - 4 x + 3 y

f (x, y) = 2^{3} - y^{2} + 2 x y + 1

y = x^{2} + 2

What is the extreme f(x)=(x-3)e^{-5x} ?
The extreme f(x)=(x-3)e^{-5x} is Maximum(16/5 , 1/(5e^{16)})