AP Calculus AB Unit 5 — Analytical Applications of Differentiation Practice Test
AP Calculus AB Unit 5 — Analytical Applications of Differentiation Practice Test
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Question 1 of 19
1. Question
Let f be the function given by f(x) = x^{ 3} . What are all values of c that satisfy the conclusion of the Mean Value Theorem on the closed interval [1,2] ?
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Question 2 of 19
2. Question
Let . Below is Rafael’s attempt to write a formal justification for the fact that the equation has a solution where ; Is Rafael’s justification complete? If not, why? Rafael’s justification:
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Question 3 of 19
3. Question
Given a function g( x) , if g ‘ ‘ ( x )=0 for a certain value of x , then g(x) has ____________________ at x.
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Question 4 of 19
4. Question
Let h ( x )=e ^{2 x−6} −e . Where does that apply. h have critical points? Choose all answers
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Question 5 of 19
5. Question
Given a function, f (x) , if f ‘ ( x )< 0 over a certain interval, then f(x) is _______________ over that interval.
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Question 6 of 19
6. Question
Let g be a function defined for all real numbers except for x=2 Also let g ‘ , the derivative of g On which intervals is g is increasing
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Question 7 of 19
7. Question
Use the sign chart for f ‘ (x) . There is/are…
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Question 8 of 19
8. Question
Let f be a polynomial function and let f ‘ , its derivative, be defined as f ‘ ( x )=x 4 ( x−2)(x +3) . At how many points does the graph of f have a relative maximum?
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Question 9 of 19
9. Question
What is the maximum value of f ( x )=x ^{3} −3 x ^{2} −1 on the interval [−3, 2] ?
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Question 10 of 19
10. Question
Let g ( x ) =2 x 3 −21 x 2 + 60 x . What is the absolute maximum value of g over the closed interval [ 0,6] .
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Question 11 of 19
11. Question
Function f is graphed. Select all the intervals where f ‘ (x)<0 and f ‘ ‘ ( x)>0 . Choose all answers that apply.
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Question 12 of 19
12. Question
The concavity of a function is described by its ____________________.
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Question 13 of 19
13. Question
Let h be a twice differentiable function, and let h (−4 )=−3,h ‘ (−4 )=0, and h ‘ ‘ (−4 )=0 . What occurs in the graph of h at the point (−4,−3) ?
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Question 14 of 19
14. Question
Let f be a twice differentiable function, and let f ( 2 )=3, f ‘ ( 2 ) =0 and f ‘ ‘ ( 2 )=5 . What occurs in the graph of g at the point (2,3) ?
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Question 15 of 19
15. Question
The twice differentiable function g and its second derivative g” are graphed What is an appropriate calculusbased justification for the fact that g has an inflection point at x=c ?
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Question 16 of 19
16. Question
Consider the function f ( x )=9−x 2 for f (x) ≥0 only. The shaded region is an isosceles triangle formed by joining the points ( 0, 0 ) , ( x , f ( x ) ) , and ( −x , f ( x ) ) , where 0 ≤ x ≤3 . What is the area of the largest triangle that satisfies the stated conditions?
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Question 17 of 19
17. Question
Kendall tried to find all the equations of vertical lines tangent to the curve given by x ^{2} +2 x y ^{2} =25 . This is her solution: Is Kendall’s solution correct? If not, at which step did she make a mistake?
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Question 18 of 19
18. Question
The derivative of a function f is given by f ‘ ( x )=ln∨x∨∙ x . On which interval is the graph of f concave up? (Use a graphing calculator)
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Question 19 of 19
19. Question
The derivative of a function
g is given by
‘
g ( x )=3 sin ( x ) +ln( x ) .CorrectIncorrect