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Popular >

extreme e^{x^3-3x}

Solution

extreme points

e^{x^{3} - 3 x}

Solution

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

Solution steps

f^{'} (x) = e^{x^{3} - 3 x} (3 x^{2} - 3)

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

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

Maximum (- 1, e^{2})

Plug

x = 1

into

e^{x^{3} - 3 x} : \frac{1}{e ^{2}}

Minimum (1, \frac{1}{e ^{2}})

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

Popular Examples

extreme y=3x^2-6x+5 extreme points

y = 3 x^{2} - 6 x + 5

extreme (2z-6)/(9z+1)extreme points

\frac{2 z - 6}{9 z + 1}

extreme f(x)=8x+2x^{-1}extreme points

f (x) = 8 x + 2 x^{- 1}

extreme f(x)=5+6x^2-4x^3 extreme points

f (x) = 5 + 6 x^{2} - 4 x^{3}

extreme f(x)=-5x^2+8x-7 extreme points

f (x) = - 5 x^{2} + 8 x - 7

Frequently Asked Questions (FAQ)

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