Student’s name:
Scores:
1
2
Total
5
4
3
I
L
1
Math 1170
Instructor: Alla Borisyuk
Midterm 2
1. Derivative f’(t) is given with a graph below.
spaces provided
a) Sketch graphs of the function f(t) itself and its second derivative in the
f’ (t)
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b) What are the critical points? Points of inflection?
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c) On which intervals does the function increasing? decreasing?
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d) On which intervals is the function concave up? concave down?
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e) If the argument t is time (in hours from the beginning of the experiment), and f(t) describes
size of a population, at what time did the population have the largest rate of growth?
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2. The number of flies in the room (N) depends on temperature (T, degrres Celcius) as
N. The level of social skills
2
20). The IQ level (Q) goes down with the number of flies as Q(N)=e
(S) depends on the IQ as S(Q)=11Q.
a) Find the derivative of S as a function of T
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b) If the temperature goes up from 20 to 21 degrees, will the level of social skills go up or down?
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3. Consider the following dynamical system:
x+i2.5x(1-x)
a) Find the steady states and their stability algebraically, using the updating function and its de
rivative
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b) What do you think will happen to the solution which starts with x
time? Sketch this solution as a function of time. (Hint: doing a quick cobwebbing drawing may
help but is not required)
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5. Find first and second derivatives of the following functions:
a) g(s)’ in(s)/s
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b) g(x)
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(Hint: simplify, and then take the derivatives)
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