Mat 116 – Business Calculus
Instructor: T. Bui
Name ________________________
Date ________________________
Quiz #2b (Sections 10.4, 10.5, 10.7)
Please circle your final answers and show your work for partial credit.
1) List 3 things that a derivative represents
2) The limit definition of f’(x) is f ' ( x)  lim
f ( x  h)  f ( x )
h
Use the above definition to find the derivative for f(x) = 2x + 3
3) Given f(x) = 5x2
a) Use the shortcut to find the derivative of f(x)
f’(x) =
b) What is the equation of the tangent line at x = 3
4) The price-demand equation and the cost function for the production of graphing calculators
are giving, respectively, by x = 5000 – 25p
and
C(x) = 70,000 + 50x
where x is the number of calculator that can be sold at a price of p per calculator and C(x) is the
total cost (in dollars) of producing x calculators
A) Express price p as a function of the demand x
B) Find the revenue function R(x) = xp using the result from part A)
C) Find the profit function in terms of x (formula: P(x) = R(x) – C(x))
D) Find the marginal profit, P’(x) using the shortcut
E) How many graphing calculators the company needs to produce and sell in order to have a
maximum profit
5) Use the shortcuts to find the derivatives of the following functions [15points]
A) f(x) = 0.32x5
f’(x) =
B) f(x) = 4x4 – 9x3 + x2 – 4x + 10
f’(x) =
C) f(x) = 7x-2
f’(x) =
2x9
D) f(x) =
3
f’(x) =
E) f(x) =
 5x
f’(x) =
F) f(x) =
f’(x) =
4
x
2
5
Formula sheet for chapter 10:
Derivative shortcuts
• If f (x) = C, then f ’(x) = 0
• If f (x) = xn, then f ’(x) = n xn-1
• If f (x) = ku(x), then f ’(x) = ku’(x)
• If f (x) = u(x) ± v(x), then f ’(x) = u’(x) ± v’(x).
Profit function: P(x) = R(x) – C(x)
Revenue function: R(x) = xp
Marginal cost function: C’(x)
Marginal revenue function: R’(x)
Marginal profit function: P’(x)
The exact cost of producing the (x + 1)st item is
C(x + 1) – C(x) or C’(x)
Average cost per unit: C ( x)  C ( x)
x
Average revenue per unit:
Average revenue per unit:
R ( x) 
R ( x)
x
P ( x) 
P ( x)
x