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Popular >

extreme (x^2-2+2)e^x

Solution

extreme points

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

Solution

Maximum (- 2, \frac{4}{e ^{2}}), Minimum (0, 0)

Solution steps

f^{'} (x) = e^{x} x^{2} + 2 x e^{x}

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 2

into

(x^{2} - 2 + 2) e^{x} : \frac{4}{e ^{2}}

Maximum (- 2, \frac{4}{e ^{2}})

Plug

x = 0

into

(x^{2} - 2 + 2) e^{x} : 0

Minimum (0, 0)

Maximum (- 2, \frac{4}{e ^{2}}), Minimum (0, 0)

Popular Examples

extreme f(x)=2x^3+9x^2+12x-9 extreme points

f (x) = 2 x^{3} + 9 x^{2} + 12 x - 9

extreme f(x,y)=7x^2-xy+10y^2 extreme points

f (x, y) = 7 x^{2} - x y + 10 y^{2}

extreme f(x)=x^3-3x^2-105x extreme points

f (x) = x^{3} - 3 x^{2} - 105 x

extreme 1/(x-3)extreme points

\frac{1}{x - 3}

extreme f(x)=x*y extreme points

f (x) = x \cdot y

Frequently Asked Questions (FAQ)

What is the extreme (x^2-2+2)e^x ?
The extreme (x^2-2+2)e^x is Maximum(-2, 4/(e^2)),Minimum(0,0)