A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 2 years ago
Hi everyone,
I'm still at high school and the level of maths there is half of the level of maths of the Single Variable Calculus course I'm following now, so there are sometimes symbols I don't understand...
What does the symbol  mean in this question:
The Derivative of x
The slope of the graph of f(x)= x changes abruptly when x = 0. Does this function have a derivative? If so, what is it? If not, why not?
Thank you!
Wiskomen.
 2 years ago
Hi everyone, I'm still at high school and the level of maths there is half of the level of maths of the Single Variable Calculus course I'm following now, so there are sometimes symbols I don't understand... What does the symbol  mean in this question: The Derivative of x The slope of the graph of f(x)= x changes abruptly when x = 0. Does this function have a derivative? If so, what is it? If not, why not? Thank you! Wiskomen.

This Question is Open

soap
 2 years ago
Best ResponseYou've already chosen the best response.1x means the absolute value of x. For example, 1 (absolute value of 1) is 1 and 1 (absolute value of negative 1) is 1. That means that the slope of the graph f(x) = x is always 1 when x > 0, and always 1 when x < 0 but when x = 0 the slope is 0. You can see this when you look at the graph of f(x) = x. This video shows an example of how to get the derivative of an absolute value function. http://www.youtube.com/watch?v=sdoBDhcEe5M

MattBenjamins
 2 years ago
Best ResponseYou've already chosen the best response.0While the above explanation of the absolute value is correct it should be noted that the absolute value function: \[f(x) = \left x \right\] is in fact not differentiable at x=0. And therefore in its entirety not differentiable. For a function to be differentiable at a certain point x0 the limits of the derivative of the function to the left side and the right side of this point have to be the same. So: \[\lim_{x \rightarrow (x_0)^} f \prime(x) = \lim_{x \rightarrow (x_0)^+} f \prime (x)\] In this case the limit of the lefthand derivative as x>0 is 1 and the limit of the righthand derivative is 1. Since they are not the same the function is not differentiable at x=0.

Wiskomen
 2 years ago
Best ResponseYou've already chosen the best response.0Thank you soap and MattBenjamins for you answers! I understand now what  means. Thanks again! Wiskomen.
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.