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Popular >

extreme y=xe^{-2x}

Solution

extreme points

y = x e^{- 2 x}

Solution

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

Solution steps

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

Find intervals:

Increasing

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

Decreasing

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

Plug

x = \frac{1}{2}

into

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

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

Popular Examples

extreme F(X,Y)=2X+3YX^2 extreme points

F (X, Y) = 2 X + 3 Y X^{2}

extreme f(x)=x+3y^2=25 extreme points

f (x) = x + 3 y^{2} = 25

extreme f(x)=110.2x-0.4x^2-20.2-2000 extreme points

f (x) = 110.2 x - 0.4 x^{2} - 20.2 - 2000

extreme f(x)=(x^3)/3-16x^2+240x-36 extreme points

f (x) = \frac{x ^{3}}{3} - 16 x^{2} + 240 x - 36

extreme y=4x^3-8x extreme points

y = 4 x^{3} - 8 x

Frequently Asked Questions (FAQ)

What is the extreme y=xe^{-2x} ?
The extreme y=xe^{-2x} is Maximum(1/2 , 1/(2e))