Use the definitional formula given below to find the derivative of the function.
Problem 1
Given y = f(x) = x^{2} + 2x +3

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

Find the value of the derivative at x = 3.
Problem 2
Given, y = f(x) = 2 x^{3} – 3x^{2} + 4x +5

Use the Power function to find derivative of the function.

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 – x^{2}
C(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 breakeven quantities.

Determine the average cost at the breakeven quantities.

Determine the marginal revenue R’(x).

Determine the marginal cost C’(x)

At what quantity is the profit maximized?