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Popular >

extreme f(x)=-x^2(x+1)^2(x-1)^2

Solution

extreme points

f (x) = - x^{2} (x + 1)^{2} (x - 1)^{2}

Solution

Maximum (- 1, 0), Minimum (- \frac{1}{3}, - \frac{4}{27}), Maximum (0, 0), Minimum (\frac{1}{3}, - \frac{4}{27}), Maximum (1, 0)

Solution steps

f^{'} (x) = - 6 x^{5} + 8 x^{3} - 2 x

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < - \frac{1}{3},

Increasing

: - \frac{1}{3} < x < 0,

Decreasing

: 0 < x < \frac{1}{3},

Increasing

: \frac{1}{3} < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

- x^{2} (x + 1)^{2} (x - 1)^{2} : 0

Maximum (- 1, 0)

Plug

x = - \frac{1}{3}

into

- x^{2} (x + 1)^{2} (x - 1)^{2} : - \frac{4}{27}

Minimum (- \frac{1}{3}, - \frac{4}{27})

Plug

x = 0

into

- x^{2} (x + 1)^{2} (x - 1)^{2} : 0

Maximum (0, 0)

Plug

x = \frac{1}{3}

into

- x^{2} (x + 1)^{2} (x - 1)^{2} : - \frac{4}{27}

Minimum (\frac{1}{3}, - \frac{4}{27})

Plug

x = 1

into

- x^{2} (x + 1)^{2} (x - 1)^{2} : 0

Maximum (1, 0)

Maximum (- 1, 0), Minimum (- \frac{1}{3}, - \frac{4}{27}), Maximum (0, 0), Minimum (\frac{1}{3}, - \frac{4}{27}), Maximum (1, 0)

Popular Examples

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f (x, y) = \frac{1}{9 - x ^{2} - y ^{2}}

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f (x, y) = 3 y^{2} - 2 y^{3} - 3 x^{2} + 6 x y

solvefor V,V=pir2h solve for

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=-x^2(x+1)^2(x-1)^2 ?
The extreme f(x)=-x^2(x+1)^2(x-1)^2 is