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Popular Functions >

extreme (x^2-3)e^x

Solution

extreme points

(x^{2} - 3) e^{x}

Solution

Maximum (- 3, \frac{6}{e ^{3}}), Minimum (1, - 2 e)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 3

into

(x^{2} - 3) e^{x} : \frac{6}{e ^{3}}

Maximum (- 3, \frac{6}{e ^{3}})

Plug

x = 1

into

(x^{2} - 3) e^{x} : - 2 e

Minimum (1, - 2 e)

Maximum (- 3, \frac{6}{e ^{3}}), Minimum (1, - 2 e)

Graph

Popular Examples

extreme f(x,y)=x^3+y^3+3xy+5

extreme f(x)=(-cos(2x))/2-2sin(x)

extreme f(x)=x^4+4x^2-10,-5<= x<= 2

extreme f(x,y)=3xy^2+x^3-3x

extreme f(x,y)=x^2+xy+y^2+x-y+1

Frequently Asked Questions (FAQ)

What is the extreme (x^2-3)e^x ?
The extreme (x^2-3)e^x is Maximum(-3, 6/(e^3)),Minimum(1,-2e)