Questions from General Calculus

Q: The figure shows graphs of f, f’, f’’, and

The figure shows graphs of f, f’, f’’, and f’’’. Identify each curve, and explain your choic...

Q: The figure shows the graphs of three functions. One is the

The figure shows the graphs of three functions. One is the position function of a car, one is the velocity of the car, and one is its acceleration. Identify each curve, and explain your choices.

Q: The figure shows the graphs of four functions. One is the

The figure shows the graphs of four functions. One is the position function of a car, one is the velocity of the car, one is its acceleration, and one is its jerk. Identify each curve, and explain you...

Q: Use the definition of a derivative to find f’(x)

Use the definition of a derivative to find f’(x) and f’’(x). Then graph f, f’, and f’’ on a common screen and check to see if your answers are reasonable. f(x) = 3x2 + 2x + 1

Q: Use the definition of a derivative to find f’(x)

Use the definition of a derivative to find f’(x) and f’’(x). Then graph f, f’, and f’’ on a common screen and check to see if your answers are reasonable. f(x) = x3 - 3x

Q: If f(x) = 2x2 - x3, find f’

If f(x) = 2x2 - x3, find f’(x), f’’(x), f’’’(x), and f(4)(x). Graph f, f’, f’’, and f’’’ on a common screen. Are the graphs consistent with the geometric interpretations of these derivatives?

Q: a. The graph of a position function of a car is

a. The graph of a position function of a car is shown, where s is measured in feet and t in seconds. Use it to graph the velocity and acceleration of the car. What is the acceleration at t = 10 second...

Q: a. Find the vertical asymptotes of the function y =

a. Find the vertical asymptotes of the function y = x2 + 1 / 3x - 2x2 b. Confirm your answer to part (a) by graphing the function.

Q: Let f(x) = ∛x . a.

Let f(x) = ∛x . a. If a ≠ 0, use Equation 2.7.5 to find f’(a). b. Show that f’(0) does not exist. c. Show that y = ∛x has a vertical tangent line at (0, 0). (Recall the shape of the graph of f. See...

Q: a. If g(x) = x2/3,

a. If g(x) = x2/3, show that g’(0) does not exist. b. If a ≠ 0, find g’(a). c. Show that y = x2/3 has a vertical tangent line at (0, 0). d. Illustrate part (c) by graphing y = x2/3.