A company that manufactures a specialty line of high performance racing boats has determined that its profit margin can be represented by the equation, PM(x)=-x^3+7x^2-10x, where x is in thousands of dollars.

Question

a) graph without technology.
b) determine the production numbers where the profit margin is negative.
c) determine the production numbers that generate a positive profit margin.
d)at what point is the profit margin greatest. ( do it in grade 12 ways)

Answer 1

PM(x)=-x^3+7x^2-10x
= -x(x^2 - 7x + 10)
= -x(x-5)(x-2)

so the x-intercepts of this function are
0, 5, and 2 and it is a cubic with a negative cubic term

Make a sketch and you should be able to answer all your questions quite readily.

Answer 2

thank u..