Chapter 5.3, Problem 37E

Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it continues on its course indefinitely. Let D(t) denote its distance from Earth after t years of travel. Do you expect that D has a limiting value?

Suppose that the second derivative of a function f is f"(x) = -(x+1)³ (x– 1)²(x – 4)°. Determine the intervals of concavity, and the x-values of any inflection points. Upload Choose a File

13. a) Determine the average rate of change over the interval x = [1, 5] of the function y = 3x + 1. b) Regardless of the interval, what will the average rate or instantaneous rate of change be for the function y = 3x + 1? Explain. Expand your answer to include linear functions in general.