Question Text: (04.05, 05.04, 07.04 HC) Must show all work to receive full credit. Consider the differential equation = 4(2x + 2) sin(x2 +2x + ). N Part A: Find the equation of the line tangent to the solution curve at the point (0, 4). (5 points) Part B: Find the second derivative at (0, 4) and use it to determine the concavity of the solution curve at that point. Explain. (10 points) Part C: Find the particular solution y = ((x) with initial condition f(0) = 4. (15 points)Question Text: (04.05, 05.04, 07.04 HC) Must show all work to receive full credit. At the start of the workday, 40,000 cubic feet of dirt was piled up at a construction site. Dirt will be added to the pile for the next 8 hours, satisfying the increasing differential equation OF = _(P-6,000), where the function Prepresents the total amount of dirt in the pile. Pis measured in cubic feet, and t is measured in hours from the start of the workday. Part A: Estimate the amount of dirt in the pile after 4 hours, using the tangent line to the graph of Pat t= 0. (10 points) Part B: Find and use to determine if what you found in Part A was an underestimate or an overestimate at t = 4. (10 points) d+2 Part C: Find the general solution to the differential equation OF = _(P -6,000). (10 points) it