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Popular >

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

Solution

extreme points

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

Solution

Minimum - \frac{2}{3}, - \frac{14 ( - \frac{2}{3} ) ^{\frac{4}{7}}}{9}, Maximum (0, 0), Minimum (\frac{2}{3}, - \frac{14 \cdot 2 ^{\frac{4}{7}}}{9 \cdot 3 ^{\frac{4}{7}}})

Solution steps

f^{'} (x) = \frac{2 ( 3 x + 2 ) ( 3 x - 2 )}{7 x ^{\frac{3}{7}}}

Find intervals:

Decreasing

: - \infty < x < - \frac{2}{3},

Increasing

: - \frac{2}{3} < x < 0,

Decreasing

: 0 < x < \frac{2}{3},

Increasing

: \frac{2}{3} < x < \infty

Plug

x = - \frac{2}{3}

into

x^{\frac{4}{7}} (x^{2} - 2) : - \frac{14 ( - \frac{2}{3} ) ^{\frac{4}{7}}}{9}

Minimum - \frac{2}{3}, - \frac{14 ( - \frac{2}{3} ) ^{\frac{4}{7}}}{9}

Plug

x = 0

into

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

Maximum (0, 0)

Plug

x = \frac{2}{3}

into

x^{\frac{4}{7}} (x^{2} - 2) : - \frac{14 \cdot 2 ^{\frac{4}{7}}}{9 \cdot 3 ^{\frac{4}{7}}}

Minimum (\frac{2}{3}, - \frac{14 \cdot 2 ^{\frac{4}{7}}}{9 \cdot 3 ^{\frac{4}{7}}})

Minimum - \frac{2}{3}, - \frac{14 ( - \frac{2}{3} ) ^{\frac{4}{7}}}{9}, Maximum (0, 0), Minimum (\frac{2}{3}, - \frac{14 \cdot 2 ^{\frac{4}{7}}}{9 \cdot 3 ^{\frac{4}{7}}})

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Frequently Asked Questions (FAQ)

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