Problem 1Given y = f(x) = x2 + 2x +3Use the definitional formula given below to

Problem 1Given y = f(x) = x2 + 2x +3Use the definitional formula given below to find the derivative of the function.Find the value of the derivative at x = 3.Problem 2Given y = f(x) = 2 x3 3×2 + 4x +5 Use the Power function to find derivative of the function.Find the value of the derivative at x = 4.Problem 3The revenue and cost functions for producing and selling quantity x for a certain production facility are given below.R(x) = 16x x2C(x) = 20 + 4x Determine the profit function P(x). Use Excel to graph the functions R(x) C(x) and P(x) for the interval 0 x 12. Copy and paste the graph below. Note: Use Scatter plot with smooth lines and markers.Compute the break-even quantities.Determine the average cost at the break-even quantities.Determine the marginal revenue R(x).Determine the marginal cost C(x)At what quantity is the profit maximized?