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Popular >

extreme (x^2-1)^3

Solution

extreme points

(x^{2} - 1)^{3}

Solution

Saddle (- 1, 0), Minimum (0, - 1), Saddle (1, 0)

Solution steps

f^{'} (x) = 6 x (x^{2} - 1)^{2}

Find intervals:

Decreasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Increasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

(x^{2} - 1)^{3} : 0

Saddle (- 1, 0)

Plug

x = 0

into

(x^{2} - 1)^{3} : - 1

Minimum (0, - 1)

Plug

x = 1

into

(x^{2} - 1)^{3} : 0

Saddle (1, 0)

Saddle (- 1, 0), Minimum (0, - 1), Saddle (1, 0)

Popular Examples

asymptotes of 2*3^x asymptotes

2 \cdot 3^{x}

intercepts of (x-4)/(x+2)intercepts

\frac{x - 4}{x + 2}

slope of 30 slope

30

critical 15-5(x+3)^2 critical points

15 - 5 (x + 3)^{2}

asymptotes of f(x)=(x^2+8x+12)/(x+2)asymptotes

f (x) = \frac{x ^{2} + 8 x + 12}{x + 2}

Frequently Asked Questions (FAQ)

What is the extreme (x^2-1)^3 ?
The extreme (x^2-1)^3 is Saddle(-1,0),Minimum(0,-1),Saddle(1,0)