QUIZ 2
Q1. The processing speed S in Ghz of a newly designed CPU depends on the processing speed s of the
previous model as in the following table.
S 2.1 2.3 2.5 2.6 2.7 2.9
s
2
3
3.1
2.1 2.2 2.3 2.4 2.5 2.6 2.7
Find an approximation for the instantaneous rates of change
d(S ◦ S)
(2.2Ghz),
ds
dS 2
(2.4Ghz),
ds
d(1/S)
(2.2Ghz),
ds
ds
(2.5Ghz)
dS
where S ◦ S denotes the composition of S with S, explaining carefully your reasoning.
Q2. The total number of cows infected by a virus grows very quickly initially until it reaches a historial
maximum then it starts decreasing slowly to a stable number. Which function among the following could
describe this behavior?
(1) f (x) = e−ax
(2) f (x) = a +
(3) f (x) = c +
bx
ecx)
1
ax+b
(4) f (x) = a log(bx) + c
Q3. The market capitalization z of a company is a function of time t andafter a change of coordinates it
has the following graph
How many critical points does the market capitalization have as a function of time and which of those are
maxima, minima or neither of these things?
For Q4.1 and Q4.2 suppose that the diameter d of the observable universe, measured in light-years, is
described according to the following graph, where t is measured in years with respect to the Earth.
1
Date: MAT135 F21 (in-person).
2
QUIZ 2
Q4.1. According to this information, is d going to increase forever? Why?
Q4.2. Is d going to become arbitrarily large as time passes or is it going to remain bounded forever? In
the second case, find an upper bound for d.
Q5. According to the following graph, how many critical points, maxima, minima and inflection points
does the function f have?
Explain your reasoning.