A=xy, P=2x +2y
P=30= 2(x+y)
15=x+y
15-x=y
SO A=(15-x)x (subbed in y=15-x)
A=15x-x^2
A’=15-2x
Area is a maximum/minimum when A’=0
0=15-2x
2x=15
x=7.5
To check that this is a max:
A’’=-2 As this is a negative value, x=7.5 is a maximum
Advice: find the equations for what you are trying to derive...