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Popular Functions >

extreme e^{2x}(x^2-3x+2)

Solution

extreme points

e^{2 x} (x^{2} - 3 x + 2)

Solution

Maximum (\frac{2 - 2}{2}, e^{2 - 2} (\frac{2 - 3}{2} + 2)), Minimum (\frac{2 + 2}{2}, e^{2 + 2} (- \frac{3 + 2}{2} + 2))

Solution steps

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

Find intervals:

Increasing

: - \infty < x < \frac{2 - 2}{2},

Decreasing

: \frac{2 - 2}{2} < x < \frac{1}{2} + 1,

Increasing

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

Plug

x = \frac{2 - 2}{2}

into

e^{2 x} (x^{2} - 3 x + 2) : e^{2 - 2} (\frac{2 - 3}{2} + 2)

Maximum (\frac{2 - 2}{2}, e^{2 - 2} (\frac{2 - 3}{2} + 2))

Plug

x = \frac{2 + 2}{2}

into

e^{2 x} (x^{2} - 3 x + 2) : e^{2 + 2} (- \frac{3 + 2}{2} + 2)

Minimum (\frac{2 + 2}{2}, e^{2 + 2} (- \frac{3 + 2}{2} + 2))

Maximum (\frac{2 - 2}{2}, e^{2 - 2} (\frac{2 - 3}{2} + 2)), Minimum (\frac{2 + 2}{2}, e^{2 + 2} (- \frac{3 + 2}{2} + 2))

Graph

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Frequently Asked Questions (FAQ)

What is the extreme e^{2x}(x^2-3x+2) ?
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