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Popular >

extreme y=x^{2/7}(x^2-4)

Solution

extreme points

y = x^{\frac{2}{7}} (x^{2} - 4)

Solution

Minimum - \frac{1}{2 ^{\frac{1}{2}}}, - \frac{7 ( - \frac{1}{2 ^{\frac{1}{2}}} ) ^{\frac{2}{7}}}{2}, Maximum (0, 0), Minimum (\frac{1}{2 ^{\frac{1}{2}}}, - \frac{7}{2 \cdot 2 ^{\frac{1}{7}}})

Solution steps

f^{'} (x) = \frac{8 ( 2 ^{\frac{1}{2}} x + 1 ) ( 2 ^{\frac{1}{2}} x - 1 )}{7 x ^{\frac{5}{7}}}

Find intervals:

Decreasing

: - \infty < x < - \frac{1}{2 ^{\frac{1}{2}}},

Increasing

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

Decreasing

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

Increasing

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

Plug

x = - \frac{1}{2 ^{\frac{1}{2}}}

into

x^{\frac{2}{7}} (x^{2} - 4) : - \frac{7 ( - \frac{1}{2 ^{\frac{1}{2}}} ) ^{\frac{2}{7}}}{2}

Minimum - \frac{1}{2 ^{\frac{1}{2}}}, - \frac{7 ( - \frac{1}{2 ^{\frac{1}{2}}} ) ^{\frac{2}{7}}}{2}

Plug

x = 0

into

x^{\frac{2}{7}} (x^{2} - 4) : 0

Maximum (0, 0)

Plug

x = \frac{1}{2 ^{\frac{1}{2}}}

into

x^{\frac{2}{7}} (x^{2} - 4) : - \frac{7}{2 \cdot 2 ^{\frac{1}{7}}}

Minimum (\frac{1}{2 ^{\frac{1}{2}}}, - \frac{7}{2 \cdot 2 ^{\frac{1}{7}}})

Minimum - \frac{1}{2 ^{\frac{1}{2}}}, - \frac{7 ( - \frac{1}{2 ^{\frac{1}{2}}} ) ^{\frac{2}{7}}}{2}, Maximum (0, 0), Minimum (\frac{1}{2 ^{\frac{1}{2}}}, - \frac{7}{2 \cdot 2 ^{\frac{1}{7}}})

Graph

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Frequently Asked Questions (FAQ)

What is the extreme y=x^{2/7}(x^2-4) ?
The extreme y=x^{2/7}(x^2-4) is