Homework SourseSuppose that a company decides to raise capital by selling s
Suppose that a company decides to raise capital by selling stock. Over the next 25 years the average monthly price of the stock fluctuates according to the rule S(t)=0.30t^1.25-1.50t+88.60 where S(t) is in dollars per share and t is the number of months since the stock was first offered for sales (this means that S(t) is only valid on the interval [0,300]. Determine the maximum and minimum prices of the stock and when these prices occured.
I found the values for x=0 is 88.60
I found x=300 is 13.16
I took the derivative of the function which is
s\'(t)=.375t^.25-1.50
but how do I set the derivative equal to 0 and solve
I found the values for x=0 is 88.60
I found x=300 is 13.16
I took the derivative of the function which is
s\'(t)=.375t^.25-1.50
but how do I set the derivative equal to 0 and solve
Solution
.375t^.25-1.50 = 0 so t = 256. s(t) = 0.30*256^(1.25) = 1.5*256 + 88.60 = 11.8 This is the minimum as f\'\'(x) >0 There is no maximum.
