Find the greatest value of function

[jd12345]

Homework Statement

If x + y = 60 and x,y >0 find greatest value of x( y-30)^2

Homework Equations

The Attempt at a Solution

I did this by the usual method that is by substituting 60 - x for y and then differentiating the function and equating derivative to zero.
I got x = 10 and x=30. At x=30 value is zero and at x=10 value is 4000 so my answer was 4000
But i checked the solution it says that greatest value does not exist
It gave the hint that limit x-->60(-) f(x) = 54000 so greatest value does not exist

I'm lost here because the function ought to have some greatest value. Help!

 

[tiny-tim]

hi jd12345!

At x=30 value is zero and at x=10 value is 4000 so my answer was 4000
But i checked the solution it says that greatest value does not exist
It gave the hint that limit x-->60(-) f(x) = 54000 so greatest value does not exist

sketch the graph …

it has a local maximum at 10, a local minimum at 30, at keeps increasing above 30

it is only defined on (0,60) (not [0,60]), so it never reaches the value it would have at 60 !

 

[jd12345]

Ok it maeks sense now - thank you