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

The extreme f(x)=(2x-1)e^{-x^2} is Minimum(-1/2 ,-2/(\sqrt[4]{e)}),Maximum(1, 1/e)

Popular >

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

extreme points

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

Minimum (- \frac{1}{2}, - \frac{2}{4 e}), Maximum (1, \frac{1}{e})

Solution steps

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

Find intervals:

Decreasing

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

Increasing

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

Decreasing

: 1 < x < \infty

Plug

x = - \frac{1}{2}

into

(2 x - 1) e^{- x^{2}} : - \frac{2}{4 e}

Minimum (- \frac{1}{2}, - \frac{2}{4 e})

Plug

x = 1

into

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

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

Minimum (- \frac{1}{2}, - \frac{2}{4 e}), Maximum (1, \frac{1}{e})

f (x) = x^{3} - 12 x^{2} + 45 x + 5

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

f (x) = - x^{\frac{5}{3}} + 5 3 x

f (x) = 2 x^{3} - 15 x^{2} - 300 x + 2

F (t) = e^{a t}

What is the extreme f(x)=(2x-1)e^{-x^2} ?
The extreme f(x)=(2x-1)e^{-x^2} is Minimum(-1/2 ,-2/(\sqrt[4]{e)}),Maximum(1, 1/e)