You are here:

Calculus/Difference Quotient


Hello, I have a test coming up this week on the difference quotient, and I'm not sure how to solve it when it involves a fraction. One of the examples my professor gave me was to find the difference quotient of f(x)= 1/m
Can you help me solve this?
Thank you in advance.

Take two points, x1 and x2.

It can be seen that f(x1) = 1/m and f(x2) = 1/m.
The difference quotient is (f(x1)-f(x2))/(x1-x2).
In this case, it is (1/m - 1/m)/(x2 - x1).
Since 1/m - 1/m = 0, this is 0/(x2-x1) = 0.

That is the answer, but to look at a more advanced case, consider the following...

If we had f(x) = 1/x, then we would get f(x1) = 1/x1 and f(x2) = 1/x2.
The difference quotient would then be (1/x1 - 1/x2)/(x1-x2).

Combining the fractions in the numerator gives [(x2-x1)/(x1*x2)]/(x1-x2).
This should be rewritten as the quotient of two fractions.
That is the same as [(x2-x1)/(x1*x2)]/[(x1-x2)/1].

Inverting the bottom and multiplying gives  [(x2-x1)/(x1*x2)]*[1/(x1-x2)].
Since (x2-x1)/(x2-x1) = -1, we have -1/(x1*x2).  


All Answers

Answers by Expert:

Ask Experts




Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology (reproduction, insusion of chemicals into bloodstream).


Experience in the area: I have tutored students in all areas of mathematics since 1980. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

Maybe not a publication, but I have respond to well oveer 8,500 questions on the PC. Well over 2,000 of them have been in calculus.

I aquired well over 40 hours of upper division courses. This was well over the number that were required. I graduated with honors in both my BS and MS degree from Oregon State University. I was allowed to jump into a few courses at college a year early.

Awards and Honors
I have been nominated as the expert of the month several times. All of my scores right now are at least a 9.8 average (out of 10).

Past/Present Clients
My past clients have been students at OSU, students at the college in South Seattle, referals from a company, friends and aquantenances, people from my church, and people like you from all over the world.

©2017 All rights reserved.

[an error occurred while processing this directive]