Download Calculus test 3.6 - 3.10(Ib)

AP Calculus AB
Test (3.6 – 3.10)
NO GRAPHING CALCULATORS
1)
Given f(x) =
a)
b)
c)
d)
e)
2)
Name: ________________
x +1
, which of the following statements are false?
x 2
f(x) has a vertical asymptote at x = 2
f(x) has a slant asymptote at y = x
f(x) has no horizontal asymptote
both b and c
none of the statements are false
x2
Given f(x) =
, which of the following statements are false?
x +1
a)
b)
c)
d)
e)
f(x) has a vertical asymptote at x = -1
f(x) has a slant asymptote at y = x - 1
f(x) has a horizontal asymptote at y = 0
both b and c
none of the statements are false
3)
Given f(x) = 4x4 – 4x2, which of the following statements are false?
a)
b)
c)
d)
e)
1
1
), (
,)
6
6
f(x) has intercepts at (0, 0), (-1, 0), and (1, 0)
f(x) has a relative maximum at (0, 0)
1
1
f(x) has a relative minimum at (, -1), (
, -1)
2
2
none of the statements are false
f(x) is concave up from (-, -
4)
The product of two positive numbers is 363. Minimize the sum of the
first and three times the second.
a)
33 and 11
b)
Both are 11 3
33
c)
22 and
2
d)
both a and b
e)
none of these
5)
An open box is to be made from a square piece of material, 24 inches on
a side, by cutting equal squares from the corners and turning up the
sides. What dimensions will give a maximum volume?
6)
Use differentials to approximate
decimal places.
Answer:
7)
4.07 ___________
Given f(x) = x3 find a tangent line approximation, T(x), at the point
(3,27). Using T(x), approximate f(x) = x3 at 3.1.
a)
b)
c)
d)
e)
8)
4.07 . Round your answer to four
29.08
29.7
29.8
29.75
none of these
Find y and dy for y = x2 when x = 2 and x = 0.01
Answer: y = _____________
Answer: dy = _____________
9)
Find the number of units x that will minimize the AVERAGE cost
function if the total cost function is C = 5x2 – 7x + 80.
a)
x = .7
b)
x=5
c)
x=4
d)
both b and c
e)
none of these
10)
11)
Find the differential, dy for y = x3 x + 1
3x 2
a)
dy =
dx
2 x +1
b)
dy = 3x2 x + 1 dx
c)
7 x 3 + 6x 2
dy =
dx
2 x +1
d)
7x3 + x2
dy =
2 x +1
e)
none of these
The radius of a sphere is measured to be 3.0 inches. If the
measurement is correct to within 0.01 inch, use differentials to
estimate the propagated error in the volume of the sphere.
a)
+ 0.000001 in3
b)
+ 0.36 in3
c)
+ 0.036 in3
d)
+ 0.06 in3
e)
none of these