Question

The sales, in millions of dollars, of a laser disc recording of a hit movie t years from the date of release is given by:

S(t) = (5t)/(t^2 + 1)

a) Find the rate at which the sales are changing at time t.

b) How fast are the sales changing at the time the laser discs are released?

Answer 1

a)

S'(t) = dS(t)/dt

S'(t) = ((d5t/dt)(t²+1) - 5t d(t²+1)/dt)/(t²+1)²

S'(t) = (5(t²+1) - 10t²)/(t²+1)²

S'(t) = (5-5t²)/(t⁴+2t²+1)