Posted by Hannah on .
A manufacturer estimates that the profit P from producing x units of a commodity is P=x^2+40x100 dollars per week. What is the maximium profit he can realize in one week?
I was going to take the derivative of the equation and set it equal to 0 and then plug it back in but it didn't work. The answer is 300 but I do not know how to get this.

Math 
MathMate,
Your approach actually works, you might have made an inversion in the sign or something.
P(x)=x²+40x100
P'(x)=2x+40=0 => x= 20
P(20)=20²+40*20100=300 QED 
Math 
Hannah,
oh ok I did I got x=20 instead of 20. Thank you!!

Math 
Hannah,
but I still do not see how you got 300.
20(2)=400 + 40(20)=800  100 = 1100? 
Math 
Ryan,
Vertex formula= b/2a
= 40/2 = 20
P(20)=(20^2)+(40*20)100
P(20)=(400)+(800)100
P(20)=300 
Math 
Ryan,
Messed up my signs alittle bit should read
P(20)=(20^2)+(40*20)100
P(20)=(400)+(800)100
P(20)=300 
Math 
MathMate,
Exactly...
P(20)=(400)+(800)100 =300 
Math 
Hannah,
oh ok so its 400. Thanks I see now