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Popular >

extreme f(x)=xe^{-3x}

Solution

extreme points

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

Solution

Maximum (\frac{1}{3}, \frac{1}{3 e})

Solution steps

f^{'} (x) = e^{- 3 x} (1 - 3 x)

Find intervals:

Increasing

: - \infty < x < \frac{1}{3},

Decreasing

: \frac{1}{3} < x < \infty

Plug

x = \frac{1}{3}

into

x e^{- 3 x} : \frac{1}{3 e}

Maximum (\frac{1}{3}, \frac{1}{3 e})

Popular Examples

extreme f(x)=121-x^2 extreme points

f (x) = 121 - x^{2}

range of f(x)=(x^3)/(x^2-4)range

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

range of (2x+3)/(x-1)range

\frac{2 x + 3}{x - 1}

inverse of f(x)=-(x+2)^2+3 inverse

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

periodicity of y=tan(x/3)periodicity

y = tan (\frac{x}{3})

Frequently Asked Questions (FAQ)

What is the extreme f(x)=xe^{-3x} ?
The extreme f(x)=xe^{-3x} is Maximum(1/3 , 1/(3e))