Question Two boats are sailing on a lake. The position of the first boat at time t is given parametrically. x₁ = 9t-10 y₁ = t2-7t-6 and the position of the second boat at time t is given by. x₁ = 3t+14 y₂ = 12 + t where t≥ 0 is the time measured in minutes and x₁xy₁, and y₂ are measured in metres. a. Find a function, f(t), for the distance between the two boats at time t. b. Using calculus and the expression found in (a) to determine, algebraically, at what time are the boats closest to each other. What is the minimum distance between the two boats? Check your value of t by substitution into the derivative. Also verify that you have found the minimum by using an appropriate calculus test.