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?