What is the extreme f(x)=-x^{5/3}+5\sqrt[3]{x} ?

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

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extreme f(x)=-x^{5/3}+5\sqrt[3]{x}

extreme points

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

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

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

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

Minimum (- 1, - 4)

Plug

x = 1

into

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

Maximum (1, 4)

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

f (x) = 2 x^{3} - 15 x^{2} - 300 x + 2

F (t) = e^{a t}

f (x) = e^{- a x}

f (x) = - x^{3} + 6 x^{2} - 9 x

f (x) = x^{2} + 9 x + 5

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