Name: ________________________ Class: ___________________ Date: __________
ID: A
Calc BC Review Chpt 3
Numeric Response
1. Find the absolute maximum value of y 
È
˘
81  x 2 on the interval ÍÍÎ 9, 9 ˙˙˚ .
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2. Find the local and absolute extreme values of the function on the given interval. Show both the first and the
second derivative test for the local.
È
˘
f (x )  x 3  6x 2  9x  1, ÍÍÎ 2, 4 ˙˙˚
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3. Find the critical numbers of the function.
x
y 2
x  25
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4. Find the inflection points for the function. Be sure to clearly show your work!!
f (x )  8x  3  2sinx, 0  x  3
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5. Find the limit.
lim
y
2  3y 2
5y 2  4y
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6. Sketch the curve. Find the equation of the slant asymptote.
y
x2
x1
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Name: ________________________
ID: A
7. The sum of two positive numbers is 16. What is the smallest possible value of the sum of their squares?
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8. The graph of the derivative f  (x ) of a continuous function f is shown. On what intervals is f decreasing?
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9. A rectangular storage container with an open top is to have a volume of 10m3 . The length of its base is twice
the width. Material for the base costs $13 per square meter. Material for the sides costs $10 per square meter.
Find the cost of the materials for the cheapest such container. Round the result to the nearest cent.
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10. Find the dimensions of the rectangle of largest area that can be inscribed in an equilateral triangle of side L =
6 cm if one side of the rectangle lies on the base of the triangle. Round each dimension to the nearest tenth.
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11. Find the most general antiderivative of the function.
f (x )  3cos x  6 sin x
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12. For what values of a and b is (2, 2.5) is an inflection point of the curve x 2 y  ax  by  0 ? What additional
inflection points does the curve have?
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Name: ________________________
ID: A
13. What is the minimum vertical distance between the parabolas y  x 2  1 and y  x  x 2 ?
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14. Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval.
È
˘
f (x )  2 x , ÍÍÎ 0, 4˙˙˚
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15. Find f.
f  (t )  2t  3 sin t, f (0)  5
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16. Find all the critical numbers of the function.
g ( )  2 cos   sin 2 
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17. Find the absolute maximum of the function.
È
˘
f (x )  sin (6x)  cos (6x) on the interval ÍÍÍÎ 0,  18 ˙˙˙˚
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18. Find an equation of the line through the point (8, 16) that cuts off the least area from the first quadrant.
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19. Find f.
f  (t )  2t  3sin t, f (0)  5
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20. Find a cubic function f (x )  ax 3  bx 2  cx  d that has a local maximum value of 112 at 1 and a local
minimum value of –1,184 at 7.
__________
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Name: ________________________
ID: A
21. Find the inflection points for the function.
f (x )  8x  3  2 sinx, 0  x  3
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22. Find the limit.
lim
x
x7  3
x6  6
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23. The sum of two positive numbers is 36. What is the smallest possible value of the sum of their squares?
__________
24. What is the shortest possible length of the line segment that is cut off by the first quadrant and is tangent to
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the curve y  at some point?
x
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25. Consider the following problem: A farmer with 800 ft of fencing wants to enclose a rectangular area and then
divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area
of the four pens?
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26. Find the most general antiderivative of the function.
f (x )  8x
1 7
 10x
1 9
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27. A particle is moving with the given data. Find the position of the particle.
v (t )  sint  cos t, s (0)  0
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Name: ________________________
ID: A
28. A steel pipe is being carried down a hallway 15 ft wide. At the end of the hall there is a right-angled turn into
a narrower hallway 9 ft wide. What is the length of the longest pipe that can be carried horizontally around
the corner?
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