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Popular >

extreme x^2e^{-3x}

Solution

extreme points

x^{2} e^{- 3 x}

Solution

Minimum (0, 0), Maximum (\frac{2}{3}, \frac{4}{9 e ^{2}})

Solution steps

f^{'} (x) = e^{- 3 x} x (2 - 3 x)

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{2}{3},

Decreasing

: \frac{2}{3} < x < \infty

Plug

x = 0

into

x^{2} e^{- 3 x} : 0

Minimum (0, 0)

Plug

x = \frac{2}{3}

into

x^{2} e^{- 3 x} : \frac{4}{9 e ^{2}}

Maximum (\frac{2}{3}, \frac{4}{9 e ^{2}})

Minimum (0, 0), Maximum (\frac{2}{3}, \frac{4}{9 e ^{2}})

Popular Examples

extreme f(x)=4x^3-2x+3 extreme points

f (x) = 4 x^{3} - 2 x + 3

extreme f(x,y)=x^2+xy+y^2-16y+85 extreme points

f (x, y) = x^{2} + x y + y^{2} - 16 y + 85

extreme f(x)=4-5x+x^2 extreme points

f (x) = 4 - 5 x + x^{2}

extreme f(x,y)=x^2+xy+y^2-19y+120 extreme points

f (x, y) = x^{2} + x y + y^{2} - 19 y + 120

extreme f(x)=5-4x-x^3 extreme points

f (x) = 5 - 4 x - x^{3}

Frequently Asked Questions (FAQ)

What is the extreme x^2e^{-3x} ?
The extreme x^2e^{-3x} is Minimum(0,0),Maximum(2/3 , 4/(9e^2))