What is the extreme 1/2 x^{2/3}(2x-5) ?

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

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extreme 1/2 x^{2/3}(2x-5)

extreme points

\frac{1}{2} x^{\frac{2}{3}} (2 x - 5)

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = 0

into

\frac{1}{2} x^{\frac{2}{3}} (2 x - 5) : 0

Maximum (0, 0)

Plug

x = 1

into

\frac{1}{2} x^{\frac{2}{3}} (2 x - 5) : - \frac{3}{2}

Minimum (1, - \frac{3}{2})

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

f (x) = x + \frac{25}{x} + 4, 1 \leq x \leq 50

f (x, y) = 400 - 4 x^{2} - 81 y^{2}

f (x) = \frac{( x + 5 )}{x ^{2} - 2 x - 35}

f (x) = 2 x - 5 y + 3

f (x) = x^{2} + 2 y^{2} + 3 x + 10

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