Question

Find the maximum value of f(x,y)=6xy subject to the constraint x+y=10. When does the maximum value of f(x,y) occur?

Answer 1

y = 10-x
6x*y = 6x*(10-x) =60x-6x^2

Answer 2

First derivative of that:
60-12x

Set equal to 0 and solve:
-12x = -60
x = 5

Answer 3

looks good smooth

Answer 4

f(5,10-5)=f(5,5)=6(5)(5)=150 is the max value right?

Answer 5

Yeah. Should be.