Let fx 3x24 x Find the zeros of f and their multiplicities

Let f(x) = 3x^2(4 - x). Find the zeros of f and their multiplicities. Sketch the graph of y = f(x), How many naming points are in the graph of f, A patient\'s reactions R(x)(R(x) ge 0) to a certain drug. the size of whose dose is x, is observed to be R(x) = 3x^2(4 - x). What is the domain of the function R(x)? What portion of the graph of f(x) the graph of R(x)?

Solution

Given price p=27 - (x/300)²

revenue function R= price * quantity

= [27 - (x/300)² ]*x

= 27x - x³/300²

a) for maximum revenue R\' = 0

27 - 3x²/300² = 0

3x²/300² = 27

x² = 9*300² = (3*300)²

x = 3*300

x = 900

b) maximum revenue is Rmax(x=900) = 27*300 - 300³/300²

= 27*300 - 300

= 300(27-1)

= 300*26

= 7800