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Popular >

extreme e^{2-x}+x^2-x/2

Solution

extreme points

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

Solution

Minimum W_{0} (\frac{e ^{\frac{7}{4}}}{2}) + \frac{1}{4}, e^{- W_{0} (\frac{e ^{\frac{7}{4}}}{2}) + \frac{7}{4}} + W_{0} (\frac{e ^{\frac{7}{4}}}{2})^{2} + \frac{1}{16} - \frac{1}{8}

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < W_{0} (\frac{e ^{\frac{7}{4}}}{2}) + \frac{1}{4},

Increasing

: W_{0} (\frac{e ^{\frac{7}{4}}}{2}) + \frac{1}{4} < x < \infty

Plug

x = W_{0} (\frac{e ^{\frac{7}{4}}}{2}) + \frac{1}{4}

into

e^{2 - x} + x^{2} - \frac{x}{2} : e^{- W_{0} (\frac{e ^{\frac{7}{4}}}{2}) + \frac{7}{4}} + W_{0} (\frac{e ^{\frac{7}{4}}}{2})^{2} + \frac{1}{16} - \frac{1}{8}

Minimum W_{0} (\frac{e ^{\frac{7}{4}}}{2}) + \frac{1}{4}, e^{- W_{0} (\frac{e ^{\frac{7}{4}}}{2}) + \frac{7}{4}} + W_{0} (\frac{e ^{\frac{7}{4}}}{2})^{2} + \frac{1}{16} - \frac{1}{8}

Graph

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Frequently Asked Questions (FAQ)

What is the extreme e^{2-x}+x^2-x/2 ?
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