What is the extreme x^{2/3}(x^2-4) ?

The extreme x^{2/3}(x^2-4) is Minimum(-1,-3),Maximum(0,0),Minimum(1,-3)

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extreme x^{2/3}(x^2-4)

extreme points

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

Minimum (- 1, - 3), Maximum (0, 0), Minimum (1, - 3)

Solution steps

f^{'} (x) = \frac{8 ( x + 1 ) ( x - 1 )}{3 x ^{\frac{1}{3}}}

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

x^{\frac{2}{3}} (x^{2} - 4) : - 3

Minimum (- 1, - 3)

Plug

x = 0

into

x^{\frac{2}{3}} (x^{2} - 4) : 0

Maximum (0, 0)

Plug

x = 1

into

x^{\frac{2}{3}} (x^{2} - 4) : - 3

Minimum (1, - 3)

Minimum (- 1, - 3), Maximum (0, 0), Minimum (1, - 3)

f (x) = e^{k x}

x^{3} - 3 x^{2} - 9 x + 230

f (x) = ln (x - y)

f (x) = 2 x^{2} + 16 x + 30

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

What is the extreme x^{2/3}(x^2-4) ?
The extreme x^{2/3}(x^2-4) is Minimum(-1,-3),Maximum(0,0),Minimum(1,-3)