Consider the initial value problem 3t2 y(0) = = 0. 3y2 - 4 Let to be the right-hand point of the interval of existence of this solution. The direction field for this equation is plotted below. (a) Use the direction field plotted below to estimate tm, What happens at tm to prevent the solution from continuing further? 3 2 1 0 -1 -2 -3 -4 -3 -2 -1 0 2 3 4 5 6 to generate (b) Consider the Runge-Kutta method to solve this initial value problem. We can use values of y for t>tm. What significance, if any, do these values have? Consider the initial value problem 3t2 y(0) = = 0. 3y2 - 4 Let to be the right-hand point of the interval of existence of this solution. The direction field for this equation is plotted below. (a) Use the direction field plotted below to estimate tm, What happens at tm to prevent the solution from continuing further? 3 2 1 0 -1 -2 -3 -4 -3 -2 -1 0 2 3 4 5 6 to generate (b) Consider the Runge-Kutta method to solve this initial value problem. We can use values of y for t>tm. What significance, if any, do these values have