10 Multiple Choice Calculus

I’m trying to study for my Calculus course and I need some help to understand this question.


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)


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?

Graph of a function that increases from negative infinity to x equals negative 1.5, decreases from x equals negative 1.5 to x equals 1.5, crossing the y axis at y equals 6, and increases from x equals 1.5 to positive infinity with x intercepts at x equals negative 3, 1 and 2. (5 points)


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.

Graph consists of 3 line segments from x equals negative 4 to x equals 4. Graph is decreasing from x equals negative 4 to x equals negative 2, increases from x equals negative 2 to x equals 2 and decreases from x equals 2 to x equals 4. There are x intercepts at x equals negative 4, 0 and 4. (5 points)


Which of the following functions grows the fastest as x grows without bound? (5 points)


Compare the growth rate of the functions f(x) = x3 + 1 and g(x) = x2 . (5 points)


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 -3 0 3 8
f ‘(x) -4 -2 0 4 5

If f ‘(x) is always increasing, which statement about f(x) must be true? (5 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)? (5 points)

x 0.1 0.2 0.3 0.4 0.5
f ‘(x) 1 2 3 -4 5


Use the graph of f(t) = 2t + 2 on the interval [-1, 4] to write the function F(x), where f of x equals the integral from 1 to x of f of t dt . (5 points)


The 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 f of x equals the integral from 0 to x of the square root of the quantity 36 minus t squared dt . (5 points)

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