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Popular >

extreme f(x)=x^7-4x^5+10

Solution

extreme points

f (x) = x^{7} - 4 x^{5} + 10

Solution

Maximum (- \frac{2 5}{7}, \frac{6400 5}{343 7} + 10), Saddle (0, 10), Minimum (\frac{2 5}{7}, - \frac{6400 5}{343 7} + 10)

Solution steps

f^{'} (x) = 7 x^{6} - 20 x^{4}

Find intervals:

Increasing

: - \infty < x < - \frac{2 5}{7},

Decreasing

: - \frac{2 5}{7} < x < 0,

Decreasing

: 0 < x < \frac{2 5}{7},

Increasing

: \frac{2 5}{7} < x < \infty

Plug

x = - \frac{2 5}{7}

into

x^{7} - 4 x^{5} + 10 : \frac{6400 5}{343 7} + 10

Maximum (- \frac{2 5}{7}, \frac{6400 5}{343 7} + 10)

Plug

x = 0

into

x^{7} - 4 x^{5} + 10 : 10

Saddle (0, 10)

Plug

x = \frac{2 5}{7}

into

x^{7} - 4 x^{5} + 10 : - \frac{6400 5}{343 7} + 10

Minimum (\frac{2 5}{7}, - \frac{6400 5}{343 7} + 10)

Maximum (- \frac{2 5}{7}, \frac{6400 5}{343 7} + 10), Saddle (0, 10), Minimum (\frac{2 5}{7}, - \frac{6400 5}{343 7} + 10)

Graph

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=x^7-4x^5+10 ?
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