SOLUTION: Market research suggests that if a particular item is priced at x dollars, then the weekly profit P(x), in thousands of dollars, is given by the function P(x)= -4+9/2x-1/2x^2 a.

Question 1060934: Market research suggests that if a particular item is priced at x dollars, then the weekly profit P(x), in thousands of dollars, is given by the function P(x)= -4+9/2x-1/2x^2
a. What price range would yield a profit for this item?
b.Profit rises when __ < x < __ , then decreases until x=
c.What price would yield the maximum profit?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
P(x)= -(1/2)x^2+(9/2)x-4, rewriting.
Derivative and set it equal to 0
-x+4.5=0
x=4.5. That would be the same as -b/2a.
Maximum profit is with x=4.5. That is -.5(20.25)+20.25-4=6.125
profit rises when 04.5
When it is greater than 0: graph it

Solve for x either with quadratic equation or factoring.
multiply the equation by -2
x^2-9x+8=0
(x-8)(x-1)=0
x=1,8, so 1 < x < 8 would yield a profit
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