Question

How do you find the local extrema for `f(x) = x sqrt( x - 3 )`?

Answer 1

There is only a minimum at `(3,0)`

Explanation:

To find the domain of the function, `sqrt(x-3)`
`x-3>=0` `=>` `x>=3`
If `f'(x)=1*sqrt(x-3)+x/(2sqrt(x-3))=(2(x-3)+x)/(2sqrt(x-3))`
`=(3x-6)/(2sqrt(x-3))`
`f'(x)=0` for `x=2`

This is incomposible since `x>=3 This is easy to understand from the graph graph{x*sqrt(x-3) [-20, 20, -10, 10]}`