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Popular >

extreme y=(x^2-3)e^x

Solution

extreme points

y = (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)

Popular Examples

extreme f(x)=x^3-3x-5 extreme points

f (x) = x^{3} - 3 x - 5

extreme f(x)=3x^2+6x+1 extreme points

f (x) = 3 x^{2} + 6 x + 1

extreme f(x)=4-3x extreme points

f (x) = 4 - 3 x

extreme f(x,y)=xy^2-27xy-27y^2 extreme points

f (x, y) = x y^{2} - 27 x y - 27 y^{2}

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

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

Frequently Asked Questions (FAQ)

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