What is the extreme f(x)=5x^{1/3}-x^{5/3} ?

The extreme f(x)=5x^{1/3}-x^{5/3} is Minimum(-1,-4),Maximum(1,4)

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extreme f(x)=5x^{1/3}-x^{5/3}

extreme points

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

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

Solution steps

f^{'} (x) = \frac{5}{3 x ^{\frac{2}{3}}} - \frac{5 x ^{\frac{2}{3}}}{3}

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

5 x^{\frac{1}{3}} - x^{\frac{5}{3}} : - 4

Minimum (- 1, - 4)

Plug

x = 1

into

5 x^{\frac{1}{3}} - x^{\frac{5}{3}} : 4

Maximum (1, 4)

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

6 x^{2} + 30 x - 84

y = r - (x - r)^{2}

f (x) = 2 x^{3} - 30 x^{2} + 96 x + 4, 0 \leq x \leq 12

f (x) = 3 x - x^{2} + 40

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

What is the extreme f(x)=5x^{1/3}-x^{5/3} ?
The extreme f(x)=5x^{1/3}-x^{5/3} is Minimum(-1,-4),Maximum(1,4)