What is the extreme e^{2x}(x^2-2) ?

The extreme e^{2x}(x^2-2) is Maximum(-2, 2/(e^4)),Minimum(1,-e^2)

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extreme e^{2x}(x^2-2)

extreme

Maximum (- 2, \frac{2}{e ^{4}}), Minimum (1, - e^{2})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 2

into

e^{2 x} (x^{2} - 2) : \frac{2}{e ^{4}}

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

Plug

x = 1

into

e^{2 x} (x^{2} - 2) : - e^{2}

Minimum (1, - e^{2})

Maximum (- 2, \frac{2}{e ^{4}}), Minimum (1, - e^{2})

What is the extreme e^{2x}(x^2-2) ?
The extreme e^{2x}(x^2-2) is Maximum(-2, 2/(e^4)),Minimum(1,-e^2)