What is the extreme y=x^{-4}*e^{x^4} ?

The extreme y=x^{-4}*e^{x^4} is Minimum(-1,e),Minimum(1,e)

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extreme y=x^{-4}*e^{x^4}

extreme points

y = x^{- 4} \cdot e^{x^{4}}

Minimum (- 1, e), Minimum (1, e)

Solution steps

f^{'} (x) = e^{x^{4}} (- \frac{4}{x ^{5}} + \frac{4}{x})

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

x^{- 4} \cdot e^{x^{4}} : e

Minimum (- 1, e)

Plug

x = 1

into

x^{- 4} \cdot e^{x^{4}} : e

Minimum (1, e)

Minimum (- 1, e), Minimum (1, e)

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

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

f (x) = \frac{2 + 4 x ^{2}}{1 - 3 x}

f (x) = 6 x + \frac{24}{x ^{2}} + 5, x > 0

f (x) = - 5 x^{+ 30 x + 1}

What is the extreme y=x^{-4}*e^{x^4} ?
The extreme y=x^{-4}*e^{x^4} is Minimum(-1,e),Minimum(1,e)