Use the definitional formula given below to find the derivative of the function

Problem 1

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.

Problem 2

Given, y = f(x) = 2 x³ - 3x² + 4x +5

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

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

Problem 3

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)

The marginal cost is,

g)      At what quantity is the profit maximized?