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Popular >

extreme x^2e^{-7x}

Solution

extreme points

x^{2} e^{- 7 x}

Solution

Minimum (0, 0), Maximum (\frac{2}{7}, \frac{4}{49 e ^{2}})

Solution steps

f^{'} (x) = e^{- 7 x} x (2 - 7 x)

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{2}{7},

Decreasing

: \frac{2}{7} < x < \infty

Plug

x = 0

into

x^{2} e^{- 7 x} : 0

Minimum (0, 0)

Plug

x = \frac{2}{7}

into

x^{2} e^{- 7 x} : \frac{4}{49 e ^{2}}

Maximum (\frac{2}{7}, \frac{4}{49 e ^{2}})

Minimum (0, 0), Maximum (\frac{2}{7}, \frac{4}{49 e ^{2}})

Graph

Popular Examples

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6 x^{2} - 24 x - 30

extreme 2x^3+3x^2-36x+1 extreme points

2 x^{3} + 3 x^{2} - 36 x + 1

extreme 4xy+2y-3x^2+3x-4y^2 extreme points

4 x y + 2 y - 3 x^{2} + 3 x - 4 y^{2}

extreme y=2x^2-8x+10 extreme points

y = 2 x^{2} - 8 x + 10

extreme x^2-2x-3 extreme points

x^{2} - 2 x - 3

Frequently Asked Questions (FAQ)

What is the extreme x^2e^{-7x} ?
The extreme x^2e^{-7x} is Minimum(0,0),Maximum(2/7 , 4/(49e^2))