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# Calculus problems (difference quotient, power rule etc)

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Assignment Problem 1
Given f(x)=x^2+2x+3
Find the difference quotient
(f(x+h)-f(x))/h
Use the definitional formula given below to find the derivative of the function.
f^' (x)=lim?(h?0)??(f(x+h)-f(x))/h?
Find the value of the derivative at x = 3.

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Assignment Problem 2
Given, f(x)=2x^3-3x^2+4x+5
Use the Power Rule to find derivative of the function.
Find the value of the derivative at x = 4.

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Assignment 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 break-even quantities.
Determine the average cost at the break-even quantities.
Determine the marginal revenue R'(x).
Determine the marginal cost C'(x)
At what quantity is the profit maximized?

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Assignment Problem 4
Manchester Co. stocks Part #567. The annual demand rate for the part is constant and known to be 4000 units/year. The part is purchased at a cost of \$4/unit from an independent supplier. The annual holding cost for Part #567 is 25% of the per-unit purchase price, per year. Every time an order is placed, a fixed cost of \$80 is incurred. (Hints: Pay close attention to units.)

What is the optimal order quantity for minimizing the average annual total cost?
The new two questions are bonus.
(10 pts) What is the optimal number of times per year for Champaign Co. to place an order?
(10 pts) What is the corresponding average annual total cost?