Maximum values for differentiation

[JakePearson]

maximum values for differentiation :(

have a few problems with these questions, can you help :)

using differentiation, find the maximum value of the following functions?

1. f(x) = -x² + x
2. f(x) = lnx - x
3. f(x) = -x² + 2x²
4. f(x) = x²/4 + 4/x
5. f(x) = xe^-2x2
6. f(x) = sqrt(x - n)/x ; n>0

hope you guys can help !

i thought it was straight forward differentiation but it aint :(

 

[rock.freak667]

At a stationary value f'(x)=0. (So find what x equals when f'(x)=0)
Say at f'(x)=0, x=a
Then find f''(a) and if f''(a)<0 then the point (x,f(a)) is a maximum.
If f''(a)>0, then (x,f(a)) is a minimum point.

 

[Pengwuino]

To add to that, you must look at every stationary value. You may find a local maximum but it might not be the only maximum or the maximum of the whole function.

 

[n!kofeyn]

At a stationary value f'(x)=0. (So find what x equals when f'(x)=0)
Say at f'(x)=0, x=a
Then find f''(a) and if f''(a)<0 then the point (x,f(a)) is a maximum.
If f''(a)>0, then (x,f(a)) is a minimum point.

That only finds the absolute max or min if there is only one critical point (a point x where f'(x)=0, what you call stationary value) in an interval. If there are multiple critical points, then this only gives you relative maxs and mins. I think the first thing JakePearson needs to do is to find the domain of each function. Most of them have domain (-∞,∞), but a few of them have specific domains.

Have you looked in your book on how to do this? Most calculus books give very specific instructions on how to find maxs and mins. When you post 6 problems without any posted work or thoughts, it doesn't show much initiative, especially when I know your book contains multiple methods for doing the problems. Can you do 1 or 3 by yourself?