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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