Asked by Samantha
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?
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?
Answers
Answered by
Graham
a)
S'(t) = dS(t)/dt
S'(t) = ((d5t/dt)(t<sup>2</sup>+1) - 5t d(t<sup>2</sup>+1)/dt)/(t<sup>2</sup>+1)<sup>2</sup>
S'(t) = (5(t<sup>2</sup>+1) - 10t<sup>2</sup>)/(t<sup>2</sup>+1)<sup>2</sup>
S'(t) = (5-5t<sup>2</sup>)/(t<sup>4</sup>+2t<sup>2</sup>+1)
S'(t) = dS(t)/dt
S'(t) = ((d5t/dt)(t<sup>2</sup>+1) - 5t d(t<sup>2</sup>+1)/dt)/(t<sup>2</sup>+1)<sup>2</sup>
S'(t) = (5(t<sup>2</sup>+1) - 10t<sup>2</sup>)/(t<sup>2</sup>+1)<sup>2</sup>
S'(t) = (5-5t<sup>2</sup>)/(t<sup>4</sup>+2t<sup>2</sup>+1)
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