Water is draining out of a tank. If the rate of the leak is modeled by Q(t)=16.78sin(0.15x-1.25)+14.6, at what time is the rate of the leak increasing the fastest?

Question

Water is draining out of a tank.

If the rate of the leak is modeled by Q(t)=16.78sin(0.15x-1.25)+14.6, at what time is the rate of the leak

increasing the fastest?

Use your calculus knowledge and show work.

Answer 1

Q'(t) = 16.78·0.15cos(0.15t - 1.25) = 0; cos(0.15t - 1.25) = 0.15t - 1.25 = π/2; t = (π/2 + 1/25)/0.15 = 18.8 sec

Q''(t) = - 16.75·0.15²sin(0.15t -1.25); Q''(18.8) = - 16.75·0.15²sin(0.15 ·18.8 - 1.25) = - 0.377 < 0.

So, at t = 18.8 sec we have maximum leak