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Popular >

extreme f(x)=x*e^x

Solution

extreme points

f (x) = x \cdot e^{x}

Solution

Minimum (- 1, - \frac{1}{e})

Solution steps

f^{'} (x) = e^{x} + e^{x} x

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < \infty

Plug

x = - 1

into

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

Minimum (- 1, - \frac{1}{e})

Graph

Popular Examples

extreme f(x)=x^3+2x^2-20x,0<= x<= 3 extreme points

f (x) = x^{3} + 2 x^{2} - 20 x, 0 \leq x \leq 3

extreme x^{13/3}-9x^{7/3}extreme points

x^{\frac{13}{3}} - 9 x^{\frac{7}{3}}

extreme f(x)=-x^3+3x-1 extreme points

f (x) = - x^{3} + 3 x - 1

extreme x^3-9x+2 extreme points

x^{3} - 9 x + 2

extreme f(x)=2x^3-9x^2-60x+8 extreme points

f (x) = 2 x^{3} - 9 x^{2} - 60 x + 8

Frequently Asked Questions (FAQ)

What is the extreme f(x)=x*e^x ?
The extreme f(x)=x*e^x is Minimum(-1,-1/e)