NO CALCULATOR d'y = y' (1 + 3x?y? ). Let y = f(x) be a particular 3) Solutions to the differential equation = xy' also satisfy 2 solution to the differential equations dx dy = xy with f(1) = 2. (a) On the axes provided, sketch a slope field for the given differential equation at the twelve points indicated. Draw a solution curve through the point (0,1). (b) Verify that 2 = y'(1 + 3x2y2). Does y = f(x) have a point of inflection at the point (1,2)? Explain. (c) Does y=f(x) have a relative minimum, relative maximum, or neither at (1,2)? Explain. (d) Write the equation of the line tangent to y = f(x) at x =1. Use this tangent to approximate the value of f(1.5). Then determine whether it is an underestimate or overestimate of the actual value of f(1.5). (e) Find the solution y = f(x) to the given differential equation with the initial condition f(1) = 2. Use your solution to find f(0)