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Popular >

extreme y=x^{6/7}(x^2-4)

Solution

extreme points

y = x^{\frac{6}{7}} (x^{2} - 4)

Solution

Minimum - (\frac{6}{5})^{\frac{1}{2}}, - \frac{14 ( - ( \frac{6}{5} ) ^{\frac{1}{2}} ) ^{\frac{6}{7}}}{5}, Maximum (0, 0), Minimum ((\frac{6}{5})^{\frac{1}{2}}, - \frac{14 \cdot 6 ^{\frac{3}{7}}}{5 \cdot 5 ^{\frac{3}{7}}})

Solution steps

f^{'} (x) = \frac{4 ( 5 ^{\frac{1}{2}} x + 6 ^{\frac{1}{2}} ) ( 5 ^{\frac{1}{2}} x - 6 ^{\frac{1}{2}} )}{7 x ^{\frac{1}{7}}}

Find intervals:

Decreasing

: - \infty < x < - (\frac{6}{5})^{\frac{1}{2}},

Increasing

: - (\frac{6}{5})^{\frac{1}{2}} < x < 0,

Decreasing

: 0 < x < (\frac{6}{5})^{\frac{1}{2}},

Increasing

: (\frac{6}{5})^{\frac{1}{2}} < x < \infty

Plug

x = - (\frac{6}{5})^{\frac{1}{2}}

into

x^{\frac{6}{7}} (x^{2} - 4) : - \frac{14 ( - ( \frac{6}{5} ) ^{\frac{1}{2}} ) ^{\frac{6}{7}}}{5}

Minimum - (\frac{6}{5})^{\frac{1}{2}}, - \frac{14 ( - ( \frac{6}{5} ) ^{\frac{1}{2}} ) ^{\frac{6}{7}}}{5}

Plug

x = 0

into

x^{\frac{6}{7}} (x^{2} - 4) : 0

Maximum (0, 0)

Plug

x = (\frac{6}{5})^{\frac{1}{2}}

into

x^{\frac{6}{7}} (x^{2} - 4) : - \frac{14 \cdot 6 ^{\frac{3}{7}}}{5 \cdot 5 ^{\frac{3}{7}}}

Minimum ((\frac{6}{5})^{\frac{1}{2}}, - \frac{14 \cdot 6 ^{\frac{3}{7}}}{5 \cdot 5 ^{\frac{3}{7}}})

Minimum - (\frac{6}{5})^{\frac{1}{2}}, - \frac{14 ( - ( \frac{6}{5} ) ^{\frac{1}{2}} ) ^{\frac{6}{7}}}{5}, Maximum (0, 0), Minimum ((\frac{6}{5})^{\frac{1}{2}}, - \frac{14 \cdot 6 ^{\frac{3}{7}}}{5 \cdot 5 ^{\frac{3}{7}}})

Graph

Popular Examples

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Frequently Asked Questions (FAQ)

What is the extreme y=x^{6/7}(x^2-4) ?
The extreme y=x^{6/7}(x^2-4) is