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