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Popular >

extreme f(x)=(x^2-1)^{1/3}

Solution

extreme points

f (x) = (x^{2} - 1)^{\frac{1}{3}}

Solution

Minimum (0, - 1)

Solution steps

f^{'} (x) = \frac{2 x}{3 ( x ^{2} - 1 ) ^{\frac{2}{3}}}

Find intervals:

Decreasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Increasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = 0

into

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

Minimum (0, - 1)

Popular Examples

extreme E(x,y)=4x^2-6x+9+y-8y^2+5 extreme points

E (x, y) = 4 x^{2} - 6 x + 9 + y - 8 y^{2} + 5

extreme f(x)=-3x^4+6x^2+1 extreme points

f (x) = - 3 x^{4} + 6 x^{2} + 1

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f (x, y) = - x^{2} + y^{3} - 4 x - 3 y + 2

extreme f(x)=4cos(x)extreme points

f (x) = 4 cos (x)

extreme f(x)=x^3+3x^2-x-3 extreme points

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

Frequently Asked Questions (FAQ)

What is the extreme f(x)=(x^2-1)^{1/3} ?
The extreme f(x)=(x^2-1)^{1/3} is Minimum(0,-1)