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Popular >

extreme f(x)=x^{11}-3x^9+2

Solution

extreme points

f (x) = x^{11} - 3 x^{9} + 2

Solution

Maximum (- \frac{3 3}{11}, \frac{9565938 3}{161051 11} + 2), Saddle (0, 2), Minimum (\frac{3 3}{11}, - \frac{9565938 3}{161051 11} + 2)

Solution steps

f^{'} (x) = 11 x^{10} - 27 x^{8}

Find intervals:

Increasing

: - \infty < x < - \frac{3 3}{11},

Decreasing

: - \frac{3 3}{11} < x < 0,

Decreasing

: 0 < x < \frac{3 3}{11},

Increasing

: \frac{3 3}{11} < x < \infty

Plug

x = - \frac{3 3}{11}

into

x^{11} - 3 x^{9} + 2 : \frac{9565938 3}{161051 11} + 2

Maximum (- \frac{3 3}{11}, \frac{9565938 3}{161051 11} + 2)

Plug

x = 0

into

x^{11} - 3 x^{9} + 2 : 2

Saddle (0, 2)

Plug

x = \frac{3 3}{11}

into

x^{11} - 3 x^{9} + 2 : - \frac{9565938 3}{161051 11} + 2

Minimum (\frac{3 3}{11}, - \frac{9565938 3}{161051 11} + 2)

Maximum (- \frac{3 3}{11}, \frac{9565938 3}{161051 11} + 2), Saddle (0, 2), Minimum (\frac{3 3}{11}, - \frac{9565938 3}{161051 11} + 2)

Graph

Popular Examples

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=x^{11}-3x^9+2 ?
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