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Popular Functions >

extreme f(x)=x^3-7x-6

Solution

extreme

Solution

Maximum (- \frac{7}{3}, - (\frac{7}{3})^{\frac{3}{2}} + 7 \frac{7}{3} - 6), Minimum (\frac{7}{3}, (\frac{7}{3})^{\frac{3}{2}} - 7 \frac{7}{3} - 6)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - \frac{7}{3},

Decreasing

: - \frac{7}{3} < x < \frac{7}{3},

Increasing

: \frac{7}{3} < x < \infty

Plug

x = - \frac{7}{3}

into

x^{3} - 7 x - 6 : - (\frac{7}{3})^{\frac{3}{2}} + 7 \frac{7}{3} - 6

Maximum (- \frac{7}{3}, - (\frac{7}{3})^{\frac{3}{2}} + 7 \frac{7}{3} - 6)

Plug

x = \frac{7}{3}

into

x^{3} - 7 x - 6 : (\frac{7}{3})^{\frac{3}{2}} - 7 \frac{7}{3} - 6

Minimum (\frac{7}{3}, (\frac{7}{3})^{\frac{3}{2}} - 7 \frac{7}{3} - 6)

Maximum (- \frac{7}{3}, - (\frac{7}{3})^{\frac{3}{2}} + 7 \frac{7}{3} - 6), Minimum (\frac{7}{3}, (\frac{7}{3})^{\frac{3}{2}} - 7 \frac{7}{3} - 6)

Graph

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=x^3-7x-6 ?
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