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Mathematics
11th -
University
Calculus Review - Applications of Derivatives
15 questions
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- 1. Multiple ChoiceIf the position function for a particle is s(t) = -t2 - t, what is the instantaneous velocity function for the particle?v(t) = -2v(t) -2t - 1v(t) = t3v(t) = -t
- 2. Multiple Choice
Where does the function, f(x) = 2x3 - 9x2 + 12x -3 have relative max/min values?
Rel max x = -1, Rel min x = 2
Rel min x = 1, Rel min x = 2
Rel max x = 1, Rel min x = 2
Rel max x = 2, Rel min x = 1
- 3. Multiple Choice
Let f be the function with derivative given by f'(x) = x2 - 2/x. On which of the following intervals is f decreasing?
(-∞, 0]
(-1, 0]
(0, ∛2]
(∛2, ∞)
- 4. Multiple ChoiceGiven a function, f(x), if f'(x)>0 over a certain interval, then f(x) is __________ over that interval.increasingdecreasingconcave upconcave down
- 5. Multiple ChoiceGiven a function g(x), if g'(x)=0 at a certain value of x, then g(x) has _____________ at x.an inflection pointa critical pointa minimuma maximum
- 6. Multiple ChoiceThe slope of a function is described by its ____________.first derivativesecond derivativethird derivativeexpression
- 7. Multiple ChoiceWhat is the maximum value of f(x) = x3 - 3x2 - 1 on the interval [-3, 2]?0-125
- 8. Multiple ChoiceIf a function has a derivative that is negative, what does that tell you?The function is increasingThe function is decreasingThe function is concave upThe function is concave down
- 9. Multiple ChoiceWhat is a point of inflection?When a function goes from increasing to decreasingWhen a function goes from concave up to concave down
- 10. Multiple ChoiceIf a function has a second derivative that is negative, what does that tell you?The function is increasingThe function is decreasingThe function is concave upThe function is concave down
- 11. Multiple ChoiceIf a function has a second derivative that is positive, what does that tell you?The function is increasingThe function is decreasingThe function is concave upThe function is concave down
- 12. Multiple ChoiceOver what interval(s) is f(x) decreasing?(-3, 1)(-∞, -5) ∪ (0, 2)(-∞, -3) ∪ (1, ∞)(-5, 0) ∪ (2, ∞)
- 13. Multiple ChoiceThe derivative f'(x) of the function f(x) is shown. On what interval(s) is the FUNCTION f(x) increasing?(-∞, -1) only( 3, ∞) only(-∞, -1) and ( 3, ∞)(1, ∞)
- 14. Multiple ChoiceFind the x-coordinate of the inflection point of f(x)=6x2-x3.-202None
- 15. Multiple ChoiceA rectangular solid that has a square base has a surface area of 150 square inches. Find the maximum volume of the solid. (use Calculus)5125150250
- Answer choicesTagsAnswer choicesTags