BC MC Non-Desmos Review (Unit 1-10)

The function f is continuous on the closed interval [0, 5]. The graph of f', the derivative of f, is shown above. On which of the following intervals is f increasing?

• [0, 1] and [2, 4]

• [0, 1] and [3, 5]

• [0, 1] and [4, 5] only

• [0, 2] and [4, 5]

• 3.870

• 8.341

• 18.017

• 22.583

• [Graph A]

• [Graph B]

• [Graph C]

• [Graph D]

Tara’s heart rate during a workout is modeled by the differentiable function h, where h(t) is measured in beats per minute and t is measured in minutes from the start of the workout. Which of the following expressions gives Tara’s average heart rate from t = 30 to t = 60?

• ∫[30 to 60] h(t) dt

• (1/30) ∫[30 to 60] h(t) dt

• (1/30) ∫[30 to 60] h'(t) dt

• (h'(30) + h'(60))/2

The function f has derivatives of all orders for all real numbers with f(2) = -1, f'(2) = 4, f''(2) = 6, and f'''(2) = 12. Using the third-degree Taylor polynomial for f about x = 2, what is the approximation of f(2.1)?

• -0.570

• -0.568

• -0.566

• -0.528

• 4.266

• 2.497

• 2.278

• 1.976

• [Diagram A]

• [Diagram B]

• [Diagram C]

• [Diagram D]

Let f be the function defined above, where k is a positive constant. For what value of k, if any, is f continuous?

• 2.081

• 2.646

• 8.550

• There is no such value of k.

Let f be a differentiable function. The figure above shows the graph of the line tangent to the graph of f at x = 0. Of the following, which must be true?

• f'(0) = -f(0)

• f'(0) < f(0)

• f'(0) = f(0)

• f'(0) > f(0)

A referee moves along a straight path on the side of an athletic field. The velocity of the referee is given by v(t) = 4(t - 6)cos(2t + 5), where t is measured in minutes and v(t) is measured in meters per minute. What is the total distance traveled by the referee, in meters, from time t = 2 to time t = 6?

• 3.933

• 14.578

• 21.667

• 29.156