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

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})

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)