I need help with these homework questions

1. Let p(t) be the price of a certain stock at time t during a particular day. When the stock reaches its highest price during the day are P'(t) and P''(t) positive or negative.

2. suppose the price p(in dollars and the weekly sales x ( in thousands of units) of a certain commodity satisfy the demand equation 8p^3 +x^2 = 59,400. Determine the rate at which sales are changing at a time when x= 180, p =15, and the price is falling at the rate of $.80 per week.

3. The profit function ( in millions) for a beverage company for the years 2010 through 2016 can be approximated by f(x) = -30x^2+720x-3295, where x=10 corresponds to the year 2010.

a. A local extremum occurs at a critical number of f. Because the derivative exists for every x, the only critical number(s) occur where the derivative is zero. Find the derivative of f(x).

f'(x)=

a local maximum profit occurred in the year =

b. The maximum profit was $ million. ( find the number)