10 Multiple Choice Calculus

The graph of f ‘(x) is continuous, positive, and has a relative maximum at x = 0. Which of the following statements must be true? (5 points)The graph of f is always concave down.The graph of f is always increasing.The graph of f has a relative maximum at x = 0. The graph of f has a relative minimum at x = 0.Below is the graph of f ‘(x), the derivative of f(x), and has x-intercepts at x = -3, x = 1, and x = 2 and a relative maximum at x = -1.5 and a relative minimum at x = 1.5. Which of the following statement is false? (5 points)f is concave up from x = -1.5 to x = 1.5.f has an inflection point at x = 1.5.f has a relative minimum at x = 2.All of these are false.The graph of y = f ‘(x), the derivative of f(x), is shown below. List the intervals where the graph of f is concave down. (5 points)(-4, -2) U (2, 4)(-2, 2)(-4, 0)(0, 4)Which of the following functions grows the fastest as x grows without bound? (5 points)f(x) = exg(x) = ecosxh(x) = They all grow at the same rate.Compare the growth rate of the functions f(x) = x3 + 1 and g(x) = x2 . (5 points)f(x) grows faster than g(x).g(x) grows faster than f(x).f(x) and g(x) grow at the same rate.It cannot be determined.f is a function that is differentiable for all reals. The value of f ‘(x) is given for several values of x in the table below. x-8-3038f ‘(x)-4-2045If f ‘(x) is always increasing, which statement about f(x) must be true? (5 points)f(x) passes through the origin.f(x) is concave downwards for all x.f(x) has a relative minimum at x = 0.f(x) has a point of inflection at x = 0.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)? (5 points) x0.10.20.30.40.5f ‘(x)123-45Cannot be determinedUse the graph of f(t) = 2t + 2 on the interval [-1, 4] to write the function F(x), where . (5 points)F(x) = x2 + 3xF(x) = x2 + 2x – 12F(x) = x2 + 2x – 3F(x) = x2 + 4x – 8The velocity of a particle moving along the x-axis is v(t) = t2 + 2t + 1, with t measured in minutes and v(t) measured in feet per minute. To the nearest foot find the total distance travelled by the particle from t = 0 to t = 2 minutes. (5 points) Find the range of the function . (5 points)[-6, 6][0, 6][0, 9?][0, 18?]