What is the extreme f(x)= 4/3 x^{3/2}-1/2 x^2 ?

The extreme f(x)= 4/3 x^{3/2}-1/2 x^2 is Minimum(0,0),Maximum(4, 8/3)

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extreme f(x)= 4/3 x^{3/2}-1/2 x^2

extreme points

f (x) = \frac{4}{3} x^{\frac{3}{2}} - \frac{1}{2} x^{2}

Minimum (0, 0), Maximum (4, \frac{8}{3})

Solution steps

f^{'} (x) = 2 x^{\frac{1}{2}} - x

Find intervals:

Increasing

: 0 < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = 0

into

\frac{4}{3} x^{\frac{3}{2}} - \frac{1}{2} x^{2} : 0

Minimum (0, 0)

Plug

x = 4

into

\frac{4}{3} x^{\frac{3}{2}} - \frac{1}{2} x^{2} : \frac{8}{3}

Maximum (4, \frac{8}{3})

Minimum (0, 0), Maximum (4, \frac{8}{3})

y = (x^{2} - 9)^{3}

f (x) = \frac{1}{x}, [1, \infty]

f (x) = - 0.1 x^{2} + 1.4 x + 98.9

f (x, y) = 6 y^{2} + 4 x^{2} + 4 x y - 16 y + 8 x

y = (lo g_{10} (5 x)) + (3 I n x^{3})

What is the extreme f(x)= 4/3 x^{3/2}-1/2 x^2 ?
The extreme f(x)= 4/3 x^{3/2}-1/2 x^2 is Minimum(0,0),Maximum(4, 8/3)