Chapter 2: Q 39 (page 238)
If ,find
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
For each function graphed in Exercises 65-68, determine the values of at which fails to be continuous and/or differentiable. At such points, determine any left or right continuity or differentiability. Sketch secant lines supporting your answers.
Use the limit you just found to calculate the exact slope of the tangent line to at . Obviously you should get the same final answer as you did earlier.
Last night Phil went jogging along Main Street. His distance from the post office t minutes after p.m. is shown in the preceding graph at the right.
(a) Give a narrative (that matches the graph) of what Phil did on his jog.
(b) Sketch a graph that represents Phil’s instantaneous velocity t minutes after p.m. Make sure you label the tick marks on the vertical axis as accurately as you can.
(c) When was Phil jogging the fastest? The slowest? When was he the farthest away from the post office? The closest to the post office?
For each function f and value in Exercises 35–44, use a sequence of approximations to estimate . Illustrate your work with an appropriate sequence of graphs of secant lines.
Differentiate in three ways. When you have completed all three parts, show that your three answers are the same:
(a) with the chain rule
(b) with the product rule but not the chain rule
(c) without the chain or product rules.
What do you think about this solution?
We value your feedback to improve our textbook solutions.
