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Popular >

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

Solution

extreme points

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

Solution

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = 3

into

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

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

Popular Examples

extreme f(x)=x^2-14x+4 extreme points

f (x) = x^{2} - 14 x + 4

extreme f(x)=x^2-14x+6 extreme points

f (x) = x^{2} - 14 x + 6

extreme f(x,y)=x^3+3xy+y^3+k extreme points

f (x, y) = x^{3} + 3 x y + y^{3} + k

extreme f(x)=5+5x-5x^2,0<= x<= 3 extreme points

f (x) = 5 + 5 x - 5 x^{2}, 0 \leq x \leq 3

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

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

Frequently Asked Questions (FAQ)

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