An object’s velocity as a function of time is given by v(t)=bt−ct3, where b and c are positive constants with appropriate units.

A. If the object starts at x=0 at time t=0, find an expression for the time when it’s again at x=0. Express answer in terms of b & c.

B. Find an expression for its acceleration at that time.
Express your answer in terms of variables b and c.

The second largest public utility in the nation is the sole provider of electricity in 32 counties of southern florida. to meet the monthly demand for electricity in these counties, which is given by the inverse demand function p = 1,200 – 4q, the utility company has set up two electric generating facilities: q1 kilowatts are produced at facility 1, and q2 kilowatts are produced at facility 2 (so q = q1 + q2). the costs of producing electricity at each facility are given by c1(q1) = 8,000 + 6q12 and c2(q2) = 6,000 + 3q22, respectively. determine the profit-maximizing amounts of electricity to produce at the two facilities, the optimal price, and the utility company’s profit