What is the extreme f(x)=2x-6x^{1/3} ?

The extreme f(x)=2x-6x^{1/3} is Minimum(-1,4),Maximum(1,-4)

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extreme f(x)=2x-6x^{1/3}

extreme

Minimum (- 1, 4), Maximum (1, - 4)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

2 x - 6 x^{\frac{1}{3}} : 4

Minimum (- 1, 4)

Plug

x = 1

into

2 x - 6 x^{\frac{1}{3}} : - 4

Maximum (1, - 4)

Minimum (- 1, 4), Maximum (1, - 4)

What is the extreme f(x)=2x-6x^{1/3} ?
The extreme f(x)=2x-6x^{1/3} is Minimum(-1,4),Maximum(1,-4)