What is the critical-2e^{-2x}(x^4-2x^3) ?

The critical-2e^{-2x}(x^4-2x^3) is x=0,x=1,x=3

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critical-2e^{-2x}(x^4-2x^3)

critical points

- 2 e^{- 2 x} (x^{4} - 2 x^{3})

x = 0, x = 1, x = 3

Solution steps

- 2 e^{- 2 x} (x^{4} - 2 x^{3})

Find where

f^{'} (x)

is equal to zero or undefined

x = 0, x = 1, x = 3

Identify critical points not in

f (x)

domain

Domain of

- 2 e^{- 2 x} (x^{4} - 2 x^{3}) : - \infty < x < \infty

All critical points are in domain

x = 0, x = 1, x = 3

f (x) = \frac{x ^{3}}{3} - x^{2} + 4

f (x) = \frac{3 x}{x ^{2} - 9}

2 x^{3} - 9 x^{2} + 12 x

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

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

What is the critical-2e^{-2x}(x^4-2x^3) ?
The critical-2e^{-2x}(x^4-2x^3) is x=0,x=1,x=3