SOLUTION: {{{P(x) = -x^3 + (27/2) x^2 - 60x + 100}}}, x ≥ 5 is an approximation of the total profit (in thousands of dollars) from the sale of x hundred thousand tires. Find the number
Algebra ->
Polynomials-and-rational-expressions
-> SOLUTION: {{{P(x) = -x^3 + (27/2) x^2 - 60x + 100}}}, x ≥ 5 is an approximation of the total profit (in thousands of dollars) from the sale of x hundred thousand tires. Find the number
Log On
Question 1041296: , x ≥ 5 is an approximation of the total profit (in thousands of dollars) from the sale of x hundred thousand tires. Find the number of hundred thousands of tires that must be sold to maximize profit.
I know the answer is 5, but how exactly do I solve this? Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website! ,x ≥ 5
----------------------------------------------
Is this in a calculus course? If so:
Find the derivative of with respect to
Set the derivative equal to zero ( by looking at it )
Which one is the maximum?
I know they say , but I still want
to know if is at a maximum
----------------------------------------
For that, take the 2nd derivative of
It will be negative for and positive for
and
Therefore the maximum is at
500,000 tires must be sold to maximize profit
------------------------
Here's the plot:
