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Popular >

extreme f(x)=e^x*x^2

Solution

extreme points

f (x) = e^{x} \cdot x^{2}

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

e^{x} \cdot x^{2} : \frac{4}{e ^{2}}

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

Plug

x = 0

into

e^{x} \cdot x^{2} : 0

Minimum (0, 0)

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

Graph

Popular Examples

extreme 3x^2+y^2-2xy+42-8y extreme points

3 x^{2} + y^{2} - 2 x y + 42 - 8 y

extreme f(x)=-(56)/(81(x+1)^{10/3)}extreme points

f (x) = - \frac{56}{81 ( x + 1 ) ^{\frac{10}{3}}}

extreme f(x)=(-1)/(x-2)extreme points

f (x) = \frac{- 1}{x - 2}

extreme f(x)=(-1)/(x-7)extreme points

f (x) = \frac{- 1}{x - 7}

extreme y=2x^3-6x+3 extreme points

y = 2 x^{3} - 6 x + 3

Frequently Asked Questions (FAQ)

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