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Math 76O-250 Calculus for Business
Self-marking Practice quiz 2
Submit over the internet by 11:59 PM on Sunday 30 September 2018
Maximum value toward semester grade is 4 pts
Methods discussed in class and in links;
CAUTION: Prof McFarland makes new tests each semester.
Average grade on Fall 2017 paper test # 2 : 30.35 Perfect = 45 See future grade prospects?

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[1] (Handout #1:)(1 pt each) If f(x) = 3x + 2 and g(x) = x2 + 1,
enter integers (such as 7, 1, 0, or -4) to find the value of:
We did these
the first day!
(a) f(+1) =
(b) f(x-1) = x +  
(c) g(x+1) = x2 + x +
(d) g(f(x)) = x2 + x +
(e) f(f(x)) = x +  
[2] The line L passes through points (0,1500) and (10,0). Enter integers below (such as 7, 0, or -4) to write an equation for L.
Scoring: 3 points for left number; 2 points for the right number
y = x +

[3]
An open-topped box with square base (as in the figure at the right) is to be built for $48. The sides of the box will cost $3 per square meter, and the bottom of the box will cost $12 per square meter. If the edge-length of the square base is "x", express the VOLUME V of the box as a function of "x" by entering integers below (such as 7, 0, or -4). Hint: use the first two sentences to express the height of the box in terms of "x".
 
V = x3 + x2 + x  
Practice similar skills with
cost and volume interchanged
[4]
(a)(3 points)Find the following limit; if the limit does not exist or is undefined, enter the letter u:
x 5
   x + 3
5 - x		   =
  (b)(2 pts) In the figure at the right are graphs of y = x2 and y = 2x + 2. Use the quadratic formula to find the two points, P and Q, where these graphs intersect. The required EXACT coordinates are not integers: enter coordinates below accurate to the 2nd decimal place (for example, "0.43" or "-3.26"). Need ideas ?
  P = ( , ),
and Q = ( , ).

[5] (5 points, but not scored in this web version) Use the LIMIT METHOD to find f '(x) if f(x) = x2 + x + 1.
The answer is : f '(x) = 2x + 1, but DO NOT USE "QUICKIE" RULES (such as the power rule) to find f '(x). Also, you must correctly use limit notation at least twice for full credit. This is the only exam problem requiring the limit method to find f '(x).
  Programming to test an answer to this question in a web page is too cumbersome, and will be omitted here. On paper tests, the LIMIT METHOD will be tested, increasing the value of the test to 45 points. See the link above for a tutorial and example.

[6] (Handout) For this question, DO NOT use the limit method, product rule, or the quotient rule. No credit if you use any of these 3 methods on paper tests. For problems [6][7][8][9] below, enter numbers accurate to the 2nd decimal place.
 
(a)(1 pt)
(On paper tests) Find f '(x) if f(x) = 1
x		 +  1 
x2		  +   1 
  (On web-test) After finding f '(x) above, enter f '(1) =
(b)(2 pts)
(On paper tests) Find f '(x) if f(x) =   . 
  (On web-test) After finding f '(x) above, enter f '(1) =
(c)(2 pts)
(On paper tests) Find f '(x) if f(x) = 



  (On web-test) After finding f '(x) above, enter f '(1) =
These 3 problems
are easy,
but be careful.
For the remaining problems on this test, you may use any rule or method for full credit, including the product and quotient rules. The limit method should be avoided because it would be very difficult to use properly.
[7]
For the function f(x) = (x + 1)5
(1 - x)4
Practice choosing the correct method?
Answer is about   - 550 ; "1377" is not correct
  (On paper tests, showing work) Find f '(x), showing work.
  (On web-test) After finding f '(x) above, enter f '(2) =

[8] Use implicit differentiation to find y' (the first derivative of y) if xy - x = y2 + 2 . Thus, do NOT first solve for "y", which would be awkward, but rather: differentiate both sides of the given equation. On paper tests, answer was given, and credit was for work only.
 
(On paper tests) Find y'(x), written in terms of variables x and y, showing work.
Review this technique?
  (On web-test) After finding y'(x) above, if x = 6 and y = 2: enter y' =

[9] For the function y = (3x-2)5
Practice choosing the correct method?
  (On paper tests, showing work) Find y"(x), showing work.
  (On web-test) After finding y"(x) above, enter y"(1) =

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