What is the extreme f(x)=6sqrt(x)-6x ?

The extreme f(x)=6sqrt(x)-6x is Maximum(0,0),Minimum(1/4 , 3/2)

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extreme f(x)=6sqrt(x)-6x

extreme points

f (x) = 6 x - 6 x

Maximum (0, 0), Minimum (\frac{1}{4}, \frac{3}{2})

Solution steps

f^{'} (x) = \frac{3}{x} - 6

Find intervals:

Decreasing

: 0 \leq x < 4,

Increasing

: 4 < x < \infty

Plug

x = 0

into

6 x - 6 x : 0

Maximum (0, 0)

Plug

x = \frac{1}{4}

into

6 x - 6 x : \frac{3}{2}

Minimum (\frac{1}{4}, \frac{3}{2})

Maximum (0, 0), Minimum (\frac{1}{4}, \frac{3}{2})

What is the extreme f(x)=6sqrt(x)-6x ?
The extreme f(x)=6sqrt(x)-6x is Maximum(0,0),Minimum(1/4 , 3/2)