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Popular >

extreme (x^2-1)e^{-2x}

Solution

extreme points

(x^{2} - 1) e^{- 2 x}

Solution

Minimum (\frac{1 - 5}{2}, e^{- 1 + 5} (\frac{3 - 5}{2} - 1)), Maximum (\frac{1 + 5}{2}, e^{- 1 - 5} (\frac{3 + 5}{2} - 1))

Solution steps

f^{'} (x) = - 2 e^{- 2 x} (x^{2} - x - 1)

Find intervals:

Decreasing

: - \infty < x < \frac{1 - 5}{2},

Increasing

: \frac{1 - 5}{2} < x < \frac{5 + 1}{2},

Decreasing

: \frac{5 + 1}{2} < x < \infty

Plug

x = \frac{1 - 5}{2}

into

(x^{2} - 1) e^{- 2 x} : e^{- 1 + 5} (\frac{3 - 5}{2} - 1)

Minimum (\frac{1 - 5}{2}, e^{- 1 + 5} (\frac{3 - 5}{2} - 1))

Plug

x = \frac{1 + 5}{2}

into

(x^{2} - 1) e^{- 2 x} : e^{- 1 - 5} (\frac{3 + 5}{2} - 1)

Maximum (\frac{1 + 5}{2}, e^{- 1 - 5} (\frac{3 + 5}{2} - 1))

Minimum (\frac{1 - 5}{2}, e^{- 1 + 5} (\frac{3 - 5}{2} - 1)), Maximum (\frac{1 + 5}{2}, e^{- 1 - 5} (\frac{3 + 5}{2} - 1))

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Frequently Asked Questions (FAQ)

What is the extreme (x^2-1)e^{-2x} ?
The extreme (x^2-1)e^{-2x} is