2017 International Practice Exam Bc Mcq

Question: The graph of a differentiable function f is shown. Which is true?

Answer: D) f’(3)<f’(0)<f’(-2)

Question: Let H(x) be an antiderivative of (x^3+ sinx)/(x^2+2). If H(5)=pi, then H(2)=?

Answer: B)-5.867

Question: The continuous function f is positive and has domain x>0. If the asymptotes of the graph of f are x=), y=2. What is true?

Answer: C) Lim as x->0 f(x)= infinity and f(x)=2

Question: A file is downloaded to a computer at a rate modeled by the differentiable function f(t), when t is time in seconds since the start of the download and f(t) is measured in megabits per second. Which of the following is the best interpretation of f’(5)=2.8?

Answer: B) At time t=5 seconds, the rate at which the file is downloaded to the computer is increasing at a rate of 2.8 megabits per second

Question: The function f has a first derivative given by f’(x)=x^4-6x^2-8x-3. In what intervals is the graph of f concave up?

Answer: A) (2,infinity) only

Question: A particle travels along a straight line with velocity v(t)= (3e^(-t/2))sin(2t) mps. what is the total distance in meters, traveled by the particle during the time 0<t<2?

Answer: D) 2.261

Question: let f be a function with derivative given by f’(x)=(x^3-8x^2+3)/(x^3+1) for -1<x<9. At what value of x does f attain a relative max?

Answer: C) 0.638

Question: the number of bacteria in a container increases at the rate of r(t) bacteria per hour. If there are 1000 bacteria at time t=0, which gives the number of bacteria at t=3 hours?

Answer: D) 1000+ 0∫3 R(t)dt

Question: The function g is continuous of the closed interval [1,4] with g(1)=5 and g(4)=8. Which guarantees there is a number C in the open interval (1,4) where g’(c)=1?

Answer: B) g is differentiable on the open interval (1,4)

Question: f’’(x)=x(x-1)^2 (x+2)^3

g’’(x)=x(x-1)^2 (x+2)^3+1

h”(x)= x(x-1)^2 (x+2)^3-1

The twice differentiable functions f,g,h have second derivatives given above. What functions have a graph with 2 points of inflection?

Answer: C)f and g only