Tangent Lines, Velocities, and Growth
Read this section for an introduction to connecting derivatives to quantities we can see in the real world. Work through practice problems 1-4.
Practice Problem Answers
If , then so the slope between and is
If , then so the slope between and is
Practice 3: The average velocity between and is feet per second.
The average velocity between and is feet per second.
The velocity at is somewhere between and , probably about the middle of this interval: .
Practice 4: (a) When days, the population is approximately bacteria. When , . The average change in population is approximately
(b) To find the rate of population growth at days, sketch the line tangent to the population curve at the point and then use and another point on the tangent line to calculate the slope of the line. Using the approximate values and , the slope of the tangent line at the point is approximately .