What is the extreme-3x^{5/3}-15x^{2/3} ?

The extreme-3x^{5/3}-15x^{2/3} is Minimum(-2,-9(-2)^{2/3}),Maximum(0,0)

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extreme-3x^{5/3}-15x^{2/3}

extreme points

- 3 x^{\frac{5}{3}} - 15 x^{\frac{2}{3}}

Minimum (- 2, - 9 (- 2)^{\frac{2}{3}}), Maximum (0, 0)

Solution steps

f^{'} (x) = \frac{- 10 - 5 x}{x ^{\frac{1}{3}}}

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 0,

Decreasing

: 0 < x < \infty

Plug

x = - 2

into

- 3 x^{\frac{5}{3}} - 15 x^{\frac{2}{3}} : - 9 (- 2)^{\frac{2}{3}}

Minimum (- 2, - 9 (- 2)^{\frac{2}{3}})

Plug

x = 0

into

- 3 x^{\frac{5}{3}} - 15 x^{\frac{2}{3}} : 0

Maximum (0, 0)

Minimum (- 2, - 9 (- 2)^{\frac{2}{3}}), Maximum (0, 0)

What is the extreme-3x^{5/3}-15x^{2/3} ?
The extreme-3x^{5/3}-15x^{2/3} is Minimum(-2,-9(-2)^{2/3}),Maximum(0,0)