What is the extreme x*e^{-x^2+1} ?

The extreme x*e^{-x^2+1} is Minimum(-1/(sqrt(2)),-sqrt(e/2)),Maximum(1/(sqrt(2)),sqrt(e/2))

extreme x*e^{-x^2+1}

extreme points

x \cdot e^{- x^{2} + 1}

Minimum (- \frac{1}{2}, - \frac{e}{2}), Maximum (\frac{1}{2}, \frac{e}{2})

Solution steps

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

Find intervals:

Decreasing

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

Increasing

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

Decreasing

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

Plug

x = - \frac{1}{2}

into

x \cdot e^{- x^{2} + 1} : - \frac{e}{2}

Minimum (- \frac{1}{2}, - \frac{e}{2})

Plug

x = \frac{1}{2}

into

x \cdot e^{- x^{2} + 1} : \frac{e}{2}

Maximum (\frac{1}{2}, \frac{e}{2})

Minimum (- \frac{1}{2}, - \frac{e}{2}), Maximum (\frac{1}{2}, \frac{e}{2})

330 x^{2} - 1320 x^{3}

f (x) = \frac{∣ x - 3 ∣}{x ^{2} - 9}

y = x^{4} ln (\frac{x}{10})

f (x) = \frac{18}{( x ^{2} - 9 )}

f (x) = x^{3} - x^{2} - x + 7, - 1 \leq x \leq 2

What is the extreme x*e^{-x^2+1} ?
The extreme x*e^{-x^2+1} is Minimum(-1/(sqrt(2)),-sqrt(e/2)),Maximum(1/(sqrt(2)),sqrt(e/2))