Find an equation of the tangent to the curve y(x) = x2 - 3x + 2 at the point (1, 2).
Question 1 options:
1) x + y = 3
2) 2x - y = 3
3) y = 2
4) x - y = 3
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Question 2 (1 point)
Find an equation of the tangent to the curve f(x) = 2x2 - 2x + 1 that has slope 2.
Question 2 options:
1) y = 2x
2) y = 2x + 1
3) y = 2x + 2
4) y = 2x - 1
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Question 3 (1 point)
Find the second derivative of the function y = 14x - 12x2
Question 3 options:
1) 14 - 12x
2) 14 - 24x
3) -24x
4) -24
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Question 4 (1 point)
If s = 2t2 + 5t - 8 represents the position of an object at time t, find the acceleration (s") of this
object at t = 2 sec.
Question 4 options:
1) 13
2) 10
3) 4
4) 8
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Question 5 (1 point)
Find the second derivative of c(x) = 9x2 + 3x - 7
Question 5 options:
1) 18x + 3
2) 0
3) 18
4) 9
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Question 6 (1 point)
Find the second derivative of k(x) = 2x3 - 7x2 + 3
Question 6 options:
1) 12x - 14
2) 14x - 8
3) 14x - 12
4) 8x - 14
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Question 7 (1 point)
In order to mimize a function f(x), one must find solutions to the equation f"(x) = 0.
Question 7 options:
True
False
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Question 8 (1 point)
Find the absolute extreme values of the function f(x) = 3x - 4 if -2 ≤ x ≤ 3
Question 8 options:
1) absolute maximum is 13 at x = 3; absolute minimum is - 2 at x = -2
2) absolute maximum is 5 at x = -2; absolute minimum is - 2 at x = 3
3) absolute maximum is 13 at x = -3; absolute minimum is - 10 at x = 2
4) absolute maximum is 5 at x = 3; absolute minimum is - 10 at x = -2
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Question 9 (1 point)
Find the absolute extreme values of the function R(x) = -x2 + 8x - 16, if 4 ≤ x ≤ 4
Question 9 options:
1) absolute maximum is 1 at x = 5; absolute minimum is 0 at 4 and 0 at x = 4
2) absolute maximum is 0 at x = 5; absolute minimum is 0 at 4 and 0 at x = 4
3) absolute maximum is 0 at x = 4; absolute minimum is 0 at 4 and 0 at x = 4
4) absolute maximum is 32 at x = 4; absolute minimum is 0 at 4 and 0 at x = 4
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Question 10 (1 point)
Determine all critical points for the function A(x) = x2 + 6x + 9
Question 10 options:
1) x = 3
2) x = -6
3) x = 0
4) x = -3
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Question 11 (1 point)
Determine all critical points for the function Q(x) = x3 - 12x + 5
Question 11 options:
1) x = -2, x = 0, and x = 2
2) x = -2 and x = 2
3) x = -2
4) x = 2
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Question 12 (1 point)
Determine all critical points for the function U(x) = 20x3 - 3x5
Question 12 options:
1) x = -2 and x = 2
2) x = -2
3) x = 2
4) x = 0, x = -2, and x = 2
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Question 13 (1 point)
Find the point(s) of inflection of the function H(t) = -2t3 + 18t2 + 49.
Question 13 options:
t=0
t=6
t = 0, 6
t=3
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Question 14 (1 point)
Calculate where the minimum value of the cost function C(x) = x2 - 20x + 300 occurs and what that
minimum value is.
Question 14 options:
1) The minimum is 1100 at x = 20
2) The minimum is 300 at x = 20
3) The minimum is 200 at x = 10
4) Not enough information given
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Question 15 (1 point)
Find the point(s) of inflection of the function P(q) = -q4 + 16q3 - 96q
Question 15 options:
q = 0, 8
q=3
Not enough information given
q = 1, 2
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Question 16 (1 point)
For which of the given intervals is the function T(r) = -3r5 + 10r3 concave down?
Question 16 options:
(-1, 0)
(0, 1)
(0, +∞)
(-∞, -1)
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Question 17 (1 point)
McX Corp. has annual revenues that can be modeled by the function R(n) = -0.02n2 + 520n, and
costs that can be modeled by the function C(n) = 200n + 100,000. What is the company's
maximum annual profit?
Question 17 options:
$1,380,000
$1,280,000
$1,480,000
$1,180,000
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Question 18 (1 point)
A TV retailer supposes that in order to sell n number of TVs, the price per unit must follow the
model p = 600 - 0.3n. The retailer also supposes that the total cost of keeping n number of TVs in
inventory is given by the model C(n) = 0.3n2 + 5,000.
How many TVs must the retailer keep in inventory and sell in order to maximize his profit?
Question 18 options:
600
500
450
750
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Question 19 (1 point)
The total cost for Soni Corp. to manufacture q DVD players is given by the function C(x) = 6q3 - q2
+ 7q + 90, where q represents the quantity of DVDs manufactured.
Find the marginal cost for Soni Corp. when it manufactures 5 DVDs.
Question 19 options:
$737
$337
$537
$447
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Question 20 (1 point)
Suppose the demand for a certain item is modeled as D(p) = -3p2 + 21p + 10, where, p represents
the price of the item in dollars. Currently the price of the item is $5.
Use marginal demand to estimate the change in demand when the price is increased by one dollar.
Question 20 options:
-9
-12
28
40
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