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Popular >

extreme xe^{-5x}

Solution

extreme points

x e^{- 5 x}

Solution

Maximum (\frac{1}{5}, \frac{1}{5 e})

Solution steps

f^{'} (x) = e^{- 5 x} (1 - 5 x)

Find intervals:

Increasing

: - \infty < x < \frac{1}{5},

Decreasing

: \frac{1}{5} < x < \infty

Plug

x = \frac{1}{5}

into

x e^{- 5 x} : \frac{1}{5 e}

Maximum (\frac{1}{5}, \frac{1}{5 e})

Graph

Popular Examples

extreme f(x)=4xy+50y-9y^2-1/10 x^2y-130 extreme points

f (x) = 4 x y + 50 y - 9 y^{2} - \frac{1}{10} x^{2} y - 130

extreme f(x)=x^4+y^4-xy extreme points

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

extreme f(x)=4x^3-108x^2+729x extreme points

f (x) = 4 x^{3} - 108 x^{2} + 729 x

extreme f(x)=4x^{3/4}-x,0<= x<= 256 extreme points

f (x) = 4 x^{\frac{3}{4}} - x, 0 \leq x \leq 256

extreme-x^3+6x^2+15x+4 extreme points

- x^{3} + 6 x^{2} + 15 x + 4

Frequently Asked Questions (FAQ)

What is the extreme xe^{-5x} ?
The extreme xe^{-5x} is Maximum(1/5 , 1/(5e))