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Popular >

extreme f(x)=x^9-3x^7+2

Solution

extreme points

f (x) = x^{9} - 3 x^{7} + 2

Solution

Maximum (- \frac{7}{3}, - (\frac{7}{3})^{\frac{9}{2}} + 3 (\frac{7}{3})^{\frac{7}{2}} + 2), Saddle (0, 2), Minimum (\frac{7}{3}, (\frac{7}{3})^{\frac{9}{2}} - 3 (\frac{7}{3})^{\frac{7}{2}} + 2)

Solution steps

f^{'} (x) = 9 x^{8} - 21 x^{6}

Find intervals:

Increasing

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

Decreasing

: - \frac{7}{3} < x < 0,

Decreasing

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

Increasing

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

Plug

x = - \frac{7}{3}

into

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

Maximum (- \frac{7}{3}, - (\frac{7}{3})^{\frac{9}{2}} + 3 (\frac{7}{3})^{\frac{7}{2}} + 2)

Plug

x = 0

into

x^{9} - 3 x^{7} + 2 : 2

Saddle (0, 2)

Plug

x = \frac{7}{3}

into

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

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

Maximum (- \frac{7}{3}, - (\frac{7}{3})^{\frac{9}{2}} + 3 (\frac{7}{3})^{\frac{7}{2}} + 2), Saddle (0, 2), Minimum (\frac{7}{3}, (\frac{7}{3})^{\frac{9}{2}} - 3 (\frac{7}{3})^{\frac{7}{2}} + 2)

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Frequently Asked Questions (FAQ)

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