What is the extreme (x+2)e^{1/x} ?

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

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extreme (x+2)e^{1/x}

extreme points

(x + 2) e^{\frac{1}{x}}

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

Solution steps

Find the critical points:

x = - 1, x = 2

Domain of

(x + 2) e^{\frac{1}{x}} : x < 0 or x > 0

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug the extreme point

x = - 1

into

(x + 2) e^{\frac{1}{x}} \Rightarrow y = \frac{1}{e}

Maximum (- 1, \frac{1}{e})

Plug the extreme point

x = 2

into

(x + 2) e^{\frac{1}{x}} \Rightarrow y = 4 e^{\frac{1}{2}}

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

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

f (x) = - 3 sin^{2} (x)

f (x) = f (x) = 9 x^{8} + 8 x^{7} - 8 x - 11

f (x) = 3 x^{2} + 12 x y + 9 y^{2} + y^{3}

f (x) = 6 x^{2} + 2, 1 \leq x \leq 2

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

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