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

Problem 1

 Given y = f(x) = x2 + 2x +3

 

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

  2. Find the value of the derivative at x = 3.

Problem 2

Given, y = f(x) = 2 x3 – 3x2 + 4x +5

 

  1. Use the Power function to find derivative of the function.

  2. 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

 

  1. Determine the profit function P(x).

  2. 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.

  3. Compute the break-even quantities.

  4. Determine the average cost at the break-even quantities.

  5. Determine the marginal revenue R’(x).

  6. Determine the marginal cost C’(x)

  7. At what quantity is the profit maximized?

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