Question

Find all relative extrema, use the second derivative test where applicable...
f(x)=6x-x^2

Answer 1

well have you found f'?

Answer 2

once we find f'
we should find for what x values f'=0 ( i would say f' dne but we don't have to work about that case)
then once we find f'
we can find derivative of f' to get f''

Answer 3

yeah i already got all of that, f''(x)=-2

Answer 4

So from there where do i go..

Answer 5

and the critical point is x=3

Answer 6

so f'=6-2x
f'=0 when x=3
and f''=-2
f''=-2 means your graph is open down x=3
so what does imply what happens at x=3?

Answer 7

right, its a relative max @ 3

Answer 8

so what i'm saying is your picture looks sorta like this
and yes