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

The extreme f(x)=(e^{x^2+x+2})/x is Maximum(-1,-e^2),Minimum(1/2 ,2e^{11/4})

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extreme f(x)=(e^{x^2+x+2})/x

extreme

Maximum (- 1, - e^{2}), Minimum (\frac{1}{2}, 2 e^{\frac{11}{4}})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Decreasing

: 0 < x < \frac{1}{2},

Increasing

: \frac{1}{2} < x < \infty

Plug

x = - 1

into

\frac{e ^{x^{2} + x + 2}}{x} : - e^{2}

Maximum (- 1, - e^{2})

Plug

x = \frac{1}{2}

into

\frac{e ^{x^{2} + x + 2}}{x} : 2 e^{\frac{11}{4}}

Minimum (\frac{1}{2}, 2 e^{\frac{11}{4}})

Maximum (- 1, - e^{2}), Minimum (\frac{1}{2}, 2 e^{\frac{11}{4}})

What is the extreme f(x)=(e^{x^2+x+2})/x ?
The extreme f(x)=(e^{x^2+x+2})/x is Maximum(-1,-e^2),Minimum(1/2 ,2e^{11/4})