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Popular >

extreme f(x)=x^5(x+1)(x-1)

Solution

extreme points

f (x) = x^{5} (x + 1) (x - 1)

Solution

Maximum (- \frac{5}{7}, \frac{50 5}{343 7}), Saddle (0, 0), Minimum (\frac{5}{7}, - \frac{50 5}{343 7})

Solution steps

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

Find intervals:

Increasing

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

Decreasing

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

Decreasing

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

Increasing

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

Plug

x = - \frac{5}{7}

into

x^{5} (x + 1) (x - 1) : \frac{50 5}{343 7}

Maximum (- \frac{5}{7}, \frac{50 5}{343 7})

Plug

x = 0

into

x^{5} (x + 1) (x - 1) : 0

Saddle (0, 0)

Plug

x = \frac{5}{7}

into

x^{5} (x + 1) (x - 1) : - \frac{50 5}{343 7}

Minimum (\frac{5}{7}, - \frac{50 5}{343 7})

Maximum (- \frac{5}{7}, \frac{50 5}{343 7}), Saddle (0, 0), Minimum (\frac{5}{7}, - \frac{50 5}{343 7})

Popular Examples

intercepts of (x^2-3x-10)/(x-5)intercepts

\frac{x ^{2} - 3 x - 10}{x - 5}

inverse of f(x)=((x+8))/(x-4)inverse

f (x) = \frac{( x + 8 )}{x - 4}

domain of-2x^2+11 domain

- 2 x^{2} + 11

slope ofintercept 12x+16y=96 slope intercept

12 x + 16 y = 96

simplify (5.5)(-2.3)simplify

(5.5) (- 2.3)

Frequently Asked Questions (FAQ)

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The extreme f(x)=x^5(x+1)(x-1) is