Question

a model for the performance of a stock is P= -2.5d^2+50d where d represents the days of trading and P is the price per share. What is the maximum price per share of stock and after how many days of trading did this price occur?

Answer 1

The maximum price per share is $250 and it happens after 10 days of trading.

Explanation:

The performance of a stock is modeled by the function:

`P(d)=-2.5d^2+50d`

Where d is the number of days of trading and P is the price per share.

To find the maximum price, we use the first derivative:

`P'(d)=-5d+50`

Equating to zero:

-5d+50=0

Solving for d:

-5d = -50

d = -50/(-5) = 10

d = 10

The price for d=10 is:

`P(10)=-2.5*10^2+50*10`

`P(10)=-2.5*100+500= 250`

The maximum price per share is $250 and it happens after 10 days of trading.