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

The inflection f(x)=(x-3)e^{-x} is (5, 2/(e^5))

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

inflection points

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

(5, \frac{2}{e ^{5}})

Solution steps

Find where

f^{''} (x)

is equal to zero or undefined

x = 5

Identify inflection points not in domain or where

f (x)

is not continuous

Domain of

(x - 3) e^{- x} : - \infty < x < \infty

All inflection points are in domain and not on domain edges

x = 5

Find intervals:

Concave Downward

: - \infty < x < 5,

Concave Upward

: 5 < x < \infty

Plug

x = 5

into

(x - 3) e^{- x} : \frac{2}{e ^{5}}

(5, \frac{2}{e ^{5}})

What is the inflection f(x)=(x-3)e^{-x} ?
The inflection f(x)=(x-3)e^{-x} is (5, 2/(e^5))