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Popular >

extreme f(x)=x(x-4)^{1/3}

Solution

extreme points

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

Solution

Minimum (3, - 3)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 3,

Increasing

: 3 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = 3

into

x (x - 4)^{\frac{1}{3}} : - 3

Minimum (3, - 3)

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=x(x-4)^{1/3} ?
The extreme f(x)=x(x-4)^{1/3} is Minimum(3,-3)