dy Use the differential equation to answer questions A-C. A calculator is NOT permitted for A or C. A) On the axis provided, sketch the slope field for the given differential equation at the 6 points provided. B) Let y = f(x) be the particular solution to the given differential equation with the initial condition f(1) = 2. Write the equation for the line tangent to the graph of y = f(x) at x = 1. Use the tangent line to approximate f(1.2). Round to THREE accurate decimal places. C) Find the particular y = f(x) to the given differential equation with initial condition f(1) = 2. Use the following scenario to answer questions D and E. A calculator is not permitted for part D. A cup of coffee is cooling on the counter. The initial temperature of the coffee is 100 F. It takes 6 minutes for the coffee to cool to 80F in a room with surrounding air temperature of 60F. D) Find the value for k (the constant of proportionality) in EXACT form AND write the equation representing the particular solution for the given scenario. NO CALCULATOR. E) Using the particular solution, determine the temperature of the coffee after 4 minutes. SHOW the equation you are inputting into your calculator. Round to the nearest degree.