Name:
SUMMER II, 2014
MATH 142:203
QUIZ - 5
• This is an individual quiz, open notes, open books.
• Read each question carefully, answer each question completely, box your answers.
• Show all of your work; no credit will be given for unsupported answers.
1. (1 pt each) Find the derivative of each function. It is not necessary to simplify the results.
a)
π
f (x) = 2
e
b)
g(x) = 2x4 + x − 5
c)
f (t) =
√
3
t4
d)
g(s) =
1 + 2s3
s2 + 2
e)
h(r) = (ex + 1)lnx
2. (2.5 pts) Find the x-values on the graph of
y = f (x) =
x2 − 1
2x
where the tangent line is perpendicular to the line y = 2x − 9.
√
3. (2.5 pts) The cost of producing a bag is given by C(x) = 5 x + 1 + 500. Each bag is sold for $20.
Find the marginal profit C 0 at x = 1000. The meaning of this problem is that the profit would
increase by approximately $ C 0 (1000) if they were to increase production to 1001 bags.