« previous next »

Author Question: What does the limit of the derivative of a function tell you? (Read 1238 times)

aero

  • Hero Member
  • *****
  • Posts: 512
on: Jun 19, 2013
Starting with the function F(x) = (x^2 - 8)/(x+3), I took the derivative of it and got (x^2+6x+8)/(x+3)^2. Then I found the limit of that as x approached infinity, and it was 1. What does that answer tell me about F(x), the original function?

And please don't post any silly answers. Thanks.


j_sun

  • Sr. Member
  • ****
  • Posts: 384
Reply #1 on: Jun 19, 2013
You did the derivative and the limit correctly.
In the limit, the slope of F is 1 means that eventually, the function F  is increasing 1 unit for every unit of x.
So the graph of F will eventual look like   F approximately =  1*x +b


Related Topics

Need homework help now?

Ask unlimited questions for free

Ask a Question
« previous next »
 

Did you know?

No drugs are available to relieve parathyroid disease. Parathyroid disease is caused by a parathyroid tumor, and it needs to be removed by surgery.

Did you know?

The oldest recorded age was 122. Madame Jeanne Calment was born in France in 1875 and died in 1997. She was a vegetarian and loved olive oil, port wine, and chocolate.

Did you know?

Stevens-Johnson syndrome and Toxic Epidermal Necrolysis syndrome are life-threatening reactions that can result in death. Complications include permanent blindness, dry-eye syndrome, lung damage, photophobia, asthma, chronic obstructive pulmonary disease, permanent loss of nail beds, scarring of mucous membranes, arthritis, and chronic fatigue syndrome. Many patients' pores scar shut, causing them to retain heat.

Did you know?

Fewer than 10% of babies are born on their exact due dates, 50% are born within 1 week of the due date, and 90% are born within 2 weeks of the date.

Did you know?

There can actually be a 25-hour time difference between certain locations in the world. The International Date Line passes between the islands of Samoa and American Samoa. It is not a straight line, but "zig-zags" around various island chains. Therefore, Samoa and nearby islands have one date, while American Samoa and nearby islands are one day behind. Daylight saving time is used in some islands, but not in others—further shifting the hours out of sync with natural time.

How to know when a function is increasing or decreasing using calculus (Part 1) How to know when a function is increasing or decreasing using calculus (Part 1)
How to reflect the quadratic function relative to the x-axis How to reflect the quadratic function relative to the x-axis
List transformations and Create a table of values for the following log function: List transformations and Create a table of values for the following log function:
Find the derivative of y = 2t^4 - 10t^2 + 13t Find the derivative of y = 2t^4 - 10t^2 + 13t
To find the derivative use product rule To find the derivative use product rule
Structure and function of human teeth. Structure and function of human teeth.
Video: Types of synapses - electrical & chemical

For a complete list of videos, visit our video library