Determine the profit function

Question

Solve the following:

Q1: Given y = f(x) = x² + 2x +3

a) Use the definitional formula given below to find the derivative of the function.

b) Find the value of the derivative at x = 3.

Q2: Given, y = f(x) = 2x³ - 3x² + 4x +5

a) Use the Power function to find derivative of the function.

b) Find the value of the derivative at x = 4.

Q3: The revenue and cost functions for producing and selling quantity x for a certain production facility are given below.

R(x) = 16x - x2

C(x) = 20 + 4x

a) Determine the profit function P(x).

b) 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.

c) Compute the break-even quantities.

d) Determine the average cost at the break-even quantities.

e) Determine the marginal revenue R'(x).

f) Determine the marginal cost C'(x)

g) At what quantity is the profit maximized?