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

The extreme x^{2/3}(5/2-x) is Minimum(0,0),Maximum(1, 3/2)

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extreme x^{2/3}(5/2-x)

extreme points

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

Minimum (0, 0), Maximum (1, \frac{3}{2})

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = 0

into

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

Minimum (0, 0)

Plug

x = 1

into

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

Maximum (1, \frac{3}{2})

Minimum (0, 0), Maximum (1, \frac{3}{2})

f (x) = 2 x^{5} + 5 x^{4}

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

f (x) = 89 e^{x^{4}} + 11

f (x) = x - \frac{1}{x}

x (x - 2)^{2}

What is the extreme x^{2/3}(5/2-x) ?
The extreme x^{2/3}(5/2-x) is Minimum(0,0),Maximum(1, 3/2)