Solution Found!
a. What is the physical meaning of the derivative of a function What is the graphical
Chapter 1, Problem r2(choose chapter or problem)
a. What is the physical meaning of the derivative of a function? What is the graphical meaning? b. For the function in Figure 1-6a, explain how f(x) is changing (increasing or decreasing, quickly or slowly) when x equals 4, 1, 3, and 5. 4 1 3 5 x f(x) Figure 1-6a c. If f(x) = 5x, find the average rate of change of f(x) from x = 2 to x = 2.1, from x = 2 to x = 2.01, and from x = 2 to x = 2.001. How close are these average rates to the instantaneous rate, 40.235947...? Do the average rates seem to be approaching this instantaneous rate as the second value of x approaches 2? Which concept of calculus is the instantaneous rate? Which concept of calculus is used to find the instantaneous rate? d. Mary Thon runs 200 m in 26 s! Her distance, d, in meters from the start at various times t, in seconds, is given in the table. Estimate her instantaneous velocity in m/s when t = 2, t = 18, and t = 24. For which time intervals did her velocity stay relatively constant? Why is the velocity at t = 24 reasonable in relation to the velocities atother times?t (s) d (m) t (s) d (m)0 0 14 892 7 16 1034 13 18 1196 33 20 1388 47 22 15410 61 24 17612 75 26 200
Questions & Answers
QUESTION:
a. What is the physical meaning of the derivative of a function? What is the graphical meaning? b. For the function in Figure 1-6a, explain how f(x) is changing (increasing or decreasing, quickly or slowly) when x equals 4, 1, 3, and 5. 4 1 3 5 x f(x) Figure 1-6a c. If f(x) = 5x, find the average rate of change of f(x) from x = 2 to x = 2.1, from x = 2 to x = 2.01, and from x = 2 to x = 2.001. How close are these average rates to the instantaneous rate, 40.235947...? Do the average rates seem to be approaching this instantaneous rate as the second value of x approaches 2? Which concept of calculus is the instantaneous rate? Which concept of calculus is used to find the instantaneous rate? d. Mary Thon runs 200 m in 26 s! Her distance, d, in meters from the start at various times t, in seconds, is given in the table. Estimate her instantaneous velocity in m/s when t = 2, t = 18, and t = 24. For which time intervals did her velocity stay relatively constant? Why is the velocity at t = 24 reasonable in relation to the velocities atother times?t (s) d (m) t (s) d (m)0 0 14 892 7 16 1034 13 18 1196 33 20 1388 47 22 15410 61 24 17612 75 26 200
ANSWER:Step 1 of 4
a) Derivative of a function: The physical meaning of the derivative of a function can be explained as the rate of change of that given function with respect to the change of the variable present in that function. Whereas, the graphical meaning of the derivative of a function can be signified as the Slope of that function.
Hence, this is the explanation.