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Popular >

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

Solution

extreme points

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

Solution

Minimum (1, 3)

Solution steps

f^{'} (x) = \frac{2 ( x - 1 )}{3 x ^{\frac{4}{3}}}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = 1

into

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

Minimum (1, 3)

Popular Examples

extreme f(x,y)=2x^3+2y^2-800x extreme points

f (x, y) = 2 x^{3} + 2 y^{2} - 800 x

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

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

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

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

extreme f(x)=x^2+(240)/x extreme points

f (x) = x^{2} + \frac{240}{x}

extreme f(x)=6x^4-8x^3-24x^2+35 extreme points

f (x) = 6 x^{4} - 8 x^{3} - 24 x^{2} + 35

Frequently Asked Questions (FAQ)

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