Quiz at the end of Chapter 4
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Becerra Gurrola, Luis
Bennett, Jasmine
Botello, Lisa
Garvin, Andrew
Hooper, Halie
Schminke, Luke
White, Maliah
KEY
1. Over the course of a 4 hour drive, a car traveled 200 miles. Which of the following statements below is a what the "mean value theorem" tells us about this situation?
When the car makes the return trip, its average speed will also be 50 miles per hour.
There must have been ONE RELATIVE MAXIMUM and ONE RELATIVE MINIMUM in the speed of the car during the 4 hour trip.
The car must have been driving at 50 miles per hour throughout the duration of the trip.
There must have been AT LEAST ONE TIME during that 4 hour period when the speed of the car was exactly 50 miles per hour.
2. What is a "critical point" of a function?
A value of x such that the function "blows up" to either infinity or negative infinity.
A value of x such that the function is equal to zero.
A point along the graph of a function at which the derivative of the function is equal to zero.
A point along the graph of a function which is an "inflection point" but the slope of the function at that point is not zero.
3. At a hospital, a nurse measures a patient's temperature and determines that it is 98.6°. Twelve hours later, the nurse on the next shift measures that patient's temperature, and she also gets a temperature of 98.6°. According to Rolle's Theorem, the function that describes the patient's temperature for the last 12 hours _______.
could have been found based on the limit of the function as the time approached 12 hours
must have at least one "critical point" during that 12 hour period
could have had a RELATIVE MAXIMUM during that 12 hour period but could NOT have had a RELATIVE MINIMUM
must have been constant over that 12 hour period
4. Suppose we know that the function f(x) has a critical point at x=a. We can determine the derivative of f(x), and we know that f'(x)<0 for x<a and f'(x)>0 for x>a. This is enough information to tell us that _____.
f(a) = 0
f(a) is a relative MINIMUM of the function f(x)
f(a) = negative infinity
f(a) = infinity
f(a) is a relative MAXIMUM of the function f(x)
5. When the second derivative of a function is positive at x=a, the function "concave _____" at x=a.
up
down
6. The function shown below has two "critical points". Find them:
x=plus or minus the square root of 3
x=1 and x=-1
x=-1 and x=0
x=0 and x=the square root of 3
7. Determine the antiderivative of the following function:
Option 1
Option 2
Option 3
Option 4
8. Which of the following is the right way to express an antiderivative as an indefinite integral? Here you should assume that F(x) is the antiderivative of f(x).
Option 1
Option 2
Option 3
Option 4
9. Evaluate the following indefinite integral:
Option 1
Option 2
Option 3
Option 4
10. Using l'Hopital's Rule, we know that the limit shown below is equal to which of the four expressions:
Option 1
Option 2
Option 3
Option 4
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