What is the extreme f(x)=x^2e^{-4x} ?

The extreme f(x)=x^2e^{-4x} is Minimum(0,0),Maximum(1/2 , 1/(4e^2))

Popular >

extreme f(x)=x^2e^{-4x}

extreme points

f (x) = x^{2} e^{- 4 x}

Minimum (0, 0), Maximum (\frac{1}{2}, \frac{1}{4 e ^{2}})

Solution steps

f^{'} (x) = 2 e^{- 4 x} x (1 - 2 x)

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

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

Decreasing

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

Plug

x = 0

into

x^{2} e^{- 4 x} : 0

Minimum (0, 0)

Plug

x = \frac{1}{2}

into

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

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

Minimum (0, 0), Maximum (\frac{1}{2}, \frac{1}{4 e ^{2}})

f (x) = 4 x^{2} + 2 y^{2} - 2 x y - 10 y - 2 x

f (x) = \frac{x ^{2} + 1}{x ^{2}}

f (x) = 2 x^{2} - 6 x^{4}

f (x) = - x^{2} + 10, - 3 \leq x \leq 4

f (x, y) = - x^{2} - y^{2} + x + 2 y - 1

What is the extreme f(x)=x^2e^{-4x} ?
The extreme f(x)=x^2e^{-4x} is Minimum(0,0),Maximum(1/2 , 1/(4e^2))