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Statistics - Derivatives

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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)
g) At what quantity is the profit maximized?

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