What is the extreme (sqrt(x)(x-3)^2)/2 ?

The extreme (sqrt(x)(x-3)^2)/2 is Minimum(0,0),Maximum(3/5 ,(72sqrt(3))/(25sqrt(5))),Minimum(3,0)

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extreme (sqrt(x)(x-3)^2)/2

extreme points

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

Minimum (0, 0), Maximum (\frac{3}{5}, \frac{72 3}{25 5}), Minimum (3, 0)

Solution steps

f^{'} (x) = \frac{5 x ^{2} - 18 x + 9}{4 x}

Find intervals:

Increasing

: 0 < x < \frac{3}{5},

Decreasing

: \frac{3}{5} < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 0

into

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

Minimum (0, 0)

Plug

x = \frac{3}{5}

into

\frac{x ( x - 3 ) ^{2}}{2} : \frac{72 3}{25 5}

Maximum (\frac{3}{5}, \frac{72 3}{25 5})

Plug

x = 3

into

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

Minimum (3, 0)

Minimum (0, 0), Maximum (\frac{3}{5}, \frac{72 3}{25 5}), Minimum (3, 0)

f (x) = - 0.1 t^{2} + 1.2 t + 98.6

f (x) = - 0.1 t^{2} + 1.2 t + 98.7

x^{4} - 2 x^{2} + 1 [- 2.2]

P (a, b) = a + b

f (x) = 3 x^{3} + 92 x^{2} - 54 x + 1

What is the extreme (sqrt(x)(x-3)^2)/2 ?
The extreme (sqrt(x)(x-3)^2)/2 is Minimum(0,0),Maximum(3/5 ,(72sqrt(3))/(25sqrt(5))),Minimum(3,0)