Extreme values Ex.2
1. Insert Q(t) = 120t + t² - t³ / 3³ in the Input bar to draw the function and press on the Enter key
2. Insert v(t)=Derivative[S] in the Input bar to draw the function of the derivative and press on the Enter key
3. Find point B as intersection of line a that crosses threw point A and is normal to x-aces and graph of the function v(t). See that that when t=10 s (the x-coordinate of the point B) the speed of leaking at the end of the 10th second is 40l/s (the y-coordinate of the point B)
4. The fluid will stop running when the speed of leaking v(t)=0. Insert Intersect[v, y = 0] in the Input bar and press on the Enter key to find the time when the liquid will stop leaking. The negative solution (point C1) is rejected. Find point C as intersection of line b that crosses threw pointC2 and is normal to x-aces and graph of the function Q(t). See that that when t=12 s (the x-coordinate of the point C) the amount of leaked fluid at the end of the 12th second is 1008l (the y-coordinate of the point C)