What is the extreme f(x)=e^{x^3-27x} ?

The extreme f(x)=e^{x^3-27x} is Maximum(-3,e^{54}),Minimum(3, 1/(e^{54)})

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extreme f(x)=e^{x^3-27x}

extreme points

f (x) = e^{x^{3} - 27 x}

Maximum (- 3, e^{54}), Minimum (3, \frac{1}{e ^{54}})

Solution steps

f^{'} (x) = e^{x^{3} - 27 x} (3 x^{2} - 27)

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 3

into

e^{x^{3} - 27 x} : e^{54}

Maximum (- 3, e^{54})

Plug

x = 3

into

e^{x^{3} - 27 x} : \frac{1}{e ^{54}}

Minimum (3, \frac{1}{e ^{54}})

Maximum (- 3, e^{54}), Minimum (3, \frac{1}{e ^{54}})

\frac{x ^{2} - 11 x + 67}{x - 9}

f (x) = 6 x^{\frac{2}{3}} - x

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

f (x, y) = 4 x^{4} + 4 y^{4} - 2 x y

f (x) = x^{2} + y^{2} - 4 x = 1

What is the extreme f(x)=e^{x^3-27x} ?
The extreme f(x)=e^{x^3-27x} is Maximum(-3,e^{54}),Minimum(3, 1/(e^{54)})