Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
AP Calculus AB Final First Semester Final – No Calculators! Name:_________________________________period:_____ 1) Find an equation of the tangent line to the graph of f(x) = -2x2 + 2x + 3 where x = 1. a) y = -4x + 2 b) y = -2x + 1 c) y = -4x2 + 2x + 1 d) y = -2x + 5 e) None of these 2) Find f’(x) when f(x) = sin34x a) 4cos34x b) 3(sin24x)(cos4x) c) 12(sin24x)(cos4x) d) cos34x e) None of these 3) Find the limit: a) b) c) d) e) 4) lim 2x 3 6x 2 5 x x3 3 2 ½ 0 13 Does not exist What is the x-coordinate of the point of inflection on the graph of y = a) b) c) d) e) 1 3 x + 5x2 + 24? 3 5 0 –10/3 –5 There is no point of inflection. Concavity does not change. 5) Let f(3) = 0, f’(3) = 6, g(3) = 1 and g’(3) = 1/3. Find h’(3) if h(x) = f(x)/g(x). a) 18 b) 6 c) –6 d) –2 e) 0 6) Find all the intervals on which the graph of the function is concave upward: f(x) = 8x3 – 2x4 a) b) c) d) e) 7) (- ∞ , 3) (- ∞, 0) (2, ∞ ) (0, 2) (-∞, ∞) None of these x 2 2x 15 x5 x 5 Find the limit: lim a) b) c) d) e) 2 0 Does not exist Indeterminate None of these 8) What is the value of the y-coordinate of the maximum of f(x) = x2 – 2x + 1 on the interval [0, 3}? 9) Find all horizontal asymptotes for f(x) = a) b) c) d) e) 4x x2 9 y=+1 y=4 y=+4 y=0 none of these x 2 2x 4 x 2 x 2 cx 10) Determine the value of c such that f(x) is continuous on the entire real line if f(x) = 11) Find the differential of y = sec3x a) (sec3x)(tan3x)dx b) 3(secx)(tanx)dx c) 3(sec23x)dx d) 3(tan23x)dx e) None of these 12) Find the values of x that give relative extrema for the function f(x) = 3x5 – 5x3. 13) 5 a) relative maximum: x = 0; relative minimum x = b) c) d) e) relative maximum: x = +1; relative minimum x = 0 relative maximum: x = 0; relative minimum x = +1 relative maximum: x = -1; relative minimum x = 1 none of these Given f(x) = a) b) c) d) e) x2 x 2 x2 4 3 , which of the following statements are true? (Multiple answers are possible) f(x) has a slant asymptote at y = x f(x) has no horizontal asymptote f(x) has a horizontal asymptote at y = 1 f(x) has vertical asymptotes at x = 2 and x = -2 f(x) has vertical asymptote at x = -2 14) The product of two positive numbers is 363. Minimize the sum of the first and three times the second. a) 33 and 11 b) 11 3 and 11 3 33 c) 22 and 2 d) 30.67 and 12 e) None of these 15) As a balloon in the shape of a sphere is being blown up, the volume is increasing at the rate of 4 cubic inches per second. At what rate is the radius increasing when the radius is 1 inch? a) 4π in/sec b) 1 in/sec 16 c) π in/sec d) 1 in/sec e) None of these