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- 1. Multiple ChoiceTRUE OR FALSE? If f is continuous on [-1,1], f(-1)=4 and f(1)= -2, then there is a zero between -1 and 1.TRUEFALSECANNOT BE DETERMINED
- 2. Multiple Choice
What is the limit?DNE2/31/4Infinity - 3. Multiple ChoiceFind the vertical asymptotes and holes of
y = (x+3) / (x-1)(x+3)Holes: None;
VA: x = 1, -3Holes: x = -3;
VA: x = 1Holes: x = -3, 1
VA: NoneHoles: x = 1
VA: x = -3 - 4. Multiple Choice
Which of the following best describes the continuity at x = 5?
Maximum
Minimum
Vertical Asymptote
Hole
- 5. Multiple ChoiceWhen f'(x) changes from positive to negative, there is(are) ...a maximum.a minimum.no extrema.
- 6. Multiple ChoiceWhen f'(x) changes from negative to positive, there is(are) ...a maximum.a minimum.no extrema.
- 7. Multiple ChoiceUse the sign chart for f'(x).
There is(are) ...a local maximum at x = -2.a local maximum at x = 4.local maxima at x = -2 and x = 4.no extrema. - 8. Multiple ChoiceUse the sign chart for f'(x) and the table of f(x). There is ...a local maximum at (-10,5).an absolute minimum at (-2,0).a local minimum at (20,7).all of the above
- 9. Multiple Choice
Does this function have a minimum, maximum, both or neither?
Minimum
Maximum
Both
Neither
- 10. Multiple Choice
Determine the minimum or maximum of the following function.
Min: -3
Max: -3
Min: 3
Max: 3
- 11. Multiple ChoiceFind the critical value(s) of
f(x) = x2 + 2x + 1.x = -1x = 2x = -1, 0x = 0 - 12. Multiple ChoiceFind the absolute maximum value of
g(x) = 3x3 + 6x2 on [-1, 1].Abs max of 8 when x = 1, abs min of -5/3 when x = -4/3Abs max of 9 when x = 1, abs min of -5/3 when x = -4/3Abs max of 9 when x = 1, abs min of 0 when x = 0Abs max of 9 when x = 1, abs min of -1 when x = -1 - 13. Multiple ChoiceHow many extrema are in the picture?2345
- 14. Multiple Choice
If (a,b) is a local minimum of the continuous and differentiable function f, then what will be true about f'(a)?
It's positive
It's negative
It's zero
Cannot be determined
- 15. Multiple Choice
Answer the relative minimum.
-1
0
1.5
-1 and 1.5
- 16. Multiple Choice
Answer the relative maximum.
-1
0
1.5
-1 and 1.5
- 17. Multiple ChoiceWhat is the average rate of change of the function below over the indicated interval?
f(x) = x2 - 3x - 28, [-4,7]011666 - 18. Multiple ChoiceWhat is the average rate of change of the function below over the indicated interval?
f(x) = 12√(x), [1,16]12 / 51036 - 19. Multiple ChoiceOver what interval(s) is f(x) increasing? (Be careful this is a graph of f'!)(-∞, -3) ∪ (1, ∞)(-3, 1)(-5, 0) ∪ (2, ∞)(-5, ∞)
- 20. Multiple ChoiceAt what x-value
( s) does f( x) have a minimum? (Be careful this is a graph of f'!)x = -3x = 1x = 5x = -3 and x = 5 - 21. Multiple ChoiceOver what interval(s) is f(x) decreasing?(-3, 1)(-∞, -5) ∪ (0, 2)(-∞, -3) ∪ (1, ∞)(-5, 0) ∪ (2, ∞)
- 22. Multiple ChoiceIf (a,b) is a local maximum, then what will be true about f''(a)?It's positiveIt's negativeIt's zeroCannot be determined
- 23. Multiple ChoiceIf (a,b) is a local minimum, then what will be true about f''(a)?It's postiveIt's negativeIt's zeroCannot be determined
- 24. Multiple ChoiceThe concavity of a function is described by its _______________.first derivativesecond derivativethird derivativeexpression
- 25. Multiple ChoiceFor a function g(x), g''(3)=-8 indicates that g(x) is ____________ at x=3.increasingdecreasingconcave upconcave down
- 26. Multiple ChoiceIdentify the interval from the derivative graph where the function is concave down(-1,1) & (3,4)(-2,4)(-3,-1) & (1,3)(-2,1) & (1,4)
- 27. Multiple ChoiceIdentify the interval from the derivative graph where the function is concave up.(-1,1) & (3,4)(-3,-2)(-2,-1)(-3,-1) & (1,3)
- 28. Multiple ChoiceGiven the following graph of f', the derivative of f. For what x-value does f have a relative minimum?x=-1 and x=4x=-3x=1x=3
- 29. Multiple ChoiceFind the x-coordinate of the inflection point of f(x)=6x2-x3.-202None
- 30. Multiple ChoiceFind where f(x)=6x2-x3 is concave up.x<2x>2x< -2x> -2
- 31. Multiple ChoiceFind where f(x)=6x2-x3 is decreasing.(-4,0)(0,4)x<0 or x>4x<-4 or x>0
- 32. Multiple ChoiceFind the x-coordinate of the relative max of f(x) = 6x2- x3-404None
- 33. Multiple ChoiceFind the interval(s) where f(x)=6x2-x3 is increasing.(-4,0)(0,4)(-∞, 0)∪(4, ∞)(-∞, -4 )∪(0, ∞)
- 34. Multiple ChoiceWhen is the velocity decreasing?0 < t < 6040 < t < 6015 < t < 40−40 < t < 0
- 35. Multiple ChoiceThe function has an absolute minimum.TrueFalse
- 36. Multiple ChoiceThe function has an relative maximum.TrueFalse
- 37. Multiple Choice
Which of the following best describes the continuity at x = 5?
Continuous
Removable Point Discontinuity
Infinite Discontinuity
Jump Discontinuity
- 38. Multiple ChoiceAssume this is a graph of f. What can you say about its first and second derivative from x=1 to x=5?f'(x) > 0 and f''(x) > 0f'(x) < 0 and f''(x) < 0f'(x) > 0 and f''(x) < 0f'(x) < 0 and f''(x) > 0
- 39. Multiple ChoiceHow many horizontal tangents would p(x) have?3214
- Answer choicesTagsAnswer choicesTags