What is the extreme f(x)=e^{x^3-3x} ?

The extreme f(x)=e^{x^3-3x} is Maximum(-1,e^2),Minimum(1, 1/(e^2))

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extreme f(x)=e^{x^3-3x}

extreme points

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

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}})

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