Question 1(Multiple Choice Worth 4 points) The graph of f '(x) is continuous and decreasing with an x-intercept at x = 0. Which of the following statements is false? O The graph of f has an inflection point at x = 0. The graph of f has a relative maximum at x = 0. The graph of f is always concave down. The graph of the second derivative is always negative.Question 2(Multiple Choice Worth 4 points) Below is the graph off '(x), the derivative of f(x), and has x-intercepts at x = 3, x = 1 and x = 2. There are horizontal tangents at x = 1.5 and x = 1.5. Which of the following statements is true? O f has a relative minimum at x = 1.5. O f has a relative maximum at x = 1.5. O f is decreasing on the interval from x = 1 to x = 2. 0 None of these is true. [C] Question 3(Multiple Choice Worth 4 points) The graph of f' (x), the derivative of f of x, is continuous for all x and consists of five line segments as shown below. Given f (-3) = 6, find the absolute maximum value of f (x) over the interval [-3, 0]. 0 3 O 4.5 0 6 O 10.5Question 4(Multiple Choice Worth 4 points) in The graph of y = f'(x), the derivative of f(x), is shown below. Given f(2) = 8, evaluate {(2). Question 5(Multiple Choice Worth 4 points) The graph below shows the graph of f (x), its derivative f '(x), and its second derivative f "(x). Which of the following is the correct statement? B O Ais f ', Bisf, Cisf". OAis f ", Bisf, Cisf'. OAis f', Bisf". C is f. OAis f, Bisf ', Cisf".Question 1(Multiple Choice Worth 4 points) Which of the following functions grows the slowest as x goes to infinity? O 5x O 5x O x5 O They all grow at the same rate.Question 2(Multiple Choice Worth 4 points) What does lim f( x) =5 show? (X)6 04X O g(x) grows faster than f(x) as x goes to infinity. Of(x) and g(x) grow at the same rate as x goes to infinity. Of(x) grows faster than g(x) as x goes to infinity. O L'Hopital's Rule must be used to determine the true limit value.Question 3(Multiple Choice Worth 4 points) Which of the following functions grows the fastest as x goes to infinity? O 2x O In (x) O sin(x) O x20Question 4(Multiple Choice Worth 4 points) Compare the rates of growth of f(x) = ecosx and g(x) = ex as x approaches infinity. Of(x) grows faster than g(x) as x goes to infinity. O g(x) grows faster than f(x) as x goes to infinity. Of(x) and g(x) grow at the same rate as x goes to infinity. O The rate of growth cannot be determined."U Question 5(Multiple Choice Worth 4 points) Which of the following functions grows at the same rate as 'x' + x ? OX3 Ox4 Question 1(Multiple Choice Worth 4 points) [a The function is continuous on the interval [10, 20] with some of its values given in the table above Estimate the average value of the function with a Trapezoidal Sum Approximation, using the intervals between those given points. x10 1215 19 20 f(x) 2 5 9 12 15 0 41750 O 7l000 O 8l400 O 5l500 Question 2(Multiple Choice Worth 4 points) The table of values below shows the rate of water consumption in gallons per hour at selected time intervals from t = 0 to t = 12. Using a Trapezoidal sum with 5 subintervals, estimate the total amount of water consumed in that time interval. X 2 5 7 11 12 (X) 5.7 5.0 2.0 1.2 0.6 0.4 O 28.5 O 35.76 56.88 None of theseQuestion 3(Multiple Choice Worth 4 points) f is a differentiable function on the interval [0, 1] and g(x) = f(2x). The table below gives values of f '(x). What is the value of g '(0.1)? X 0.1 0.2 0.3 0.4 0.5 f '(x) 1 2 3 5 O-4 0 4 02 O Cannot be determinedQuestion 4 (Fill-In-The-Blank Worth 4 points) f(x) and g(x) are a differentiable function for all reals and h(x) = g[f(5x)]. The table below gives selected values for f(x), g(x), f'(x), and g '(x). Find the value of h'(1). X 2 3 4 5 6 f(x) 0 2 1 20 g(x 1 3 2 6 5 0 f' ( x ) 3 2 1 4 0 2 g '(x) 5 4 3 2 0 Numerical Answers Expected! Answer for Blank 1:Question 5 (Fill- n-The-Blank Worth 4 points) The function f is continuous on the interval [3, 13] with selected values of x and f(x) given in the table below. Use the data in the table to approximate f '(3.5). x3471013 f(x) 2 8 1O 12 22 Numerical Answers Expected! Answer for Blank 1: [E2] Ti Question 1(Multiple Choice Worth 4 points) I Find the range of the function F(x)- HiePm. .4 O [0, 411] O [0, 811] Question 2(Multiple Choice Worth 4 points) Let F(x) = [ In(t2)dt . Use your calculator to find F"(1). O 12 0 6 04 OQuestion 3 (Fill-In-The-Blank Worth 4 points) Cleaning pumps remove oil at the rate modeled by the function R, given by R(t) = 2+cost with t measure in hours and and R(t) measured in gallons per hour. How much oil will the pumping stations remove during the 6-hour period from t = 0 to t = 6? Give 3 decimal places. Answer for Blank 1:Question 4(Multiple Choice Worth 4 points) Use the graph of f(t) = 2t + 3 on the interval [-3, 6] to write the function F(x), where F(x) = ff(t)at. OF(x) = 2x2 + 6x OF(x) = 2x + 3 OF(x) = x2 + 3x + 54 OF(x) = x2 + 3x - 18Question 5(Multiple Choice Worth 4 points) [[21 A particle moves along the x-axis with velocity v(t) = sin(2t), with t measured in seconds and v(t) measured in feet per second. Find the total distance travelled by the particle from t = 0 to t = 11 seconds. 02