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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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}})

16 x - 48 - 3

\frac{4 x + 3}{2 x + 5}

f (x) = x^{3} - 6 x^{2} + 9 x + 5

\frac{x ^{2} - 6 x + 8}{x ^{2} - 16}

f (n) = \frac{1}{9} n - \frac{4}{9}

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