A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 3 years ago
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?
Explanation is given in the course material, but not clear...Why cant the tangent line be defined at (0,0)...
anonymous
 3 years ago
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? Explanation is given in the course material, but not clear...Why cant the tangent line be defined at (0,0)...

This Question is Open

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0The function is not continuous at 0 so the derivative can't be taken. The two sided limit as x > 0 does not exist. As the function is elsewhere linear, its derivative is constant. For x < o it is 1 for x > 0 it is 1.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0the function is continuous but hasn't a derivative because: \[\lim_{x \rightarrow 0}[f(x+\Delta x)f(x)/\Delta x] \neq \lim_{x \rightarrow +0}[f(x+\Delta x)f(x)/\Delta x] \] for x<0 we have :\[f(x+\Delta x)f(x)/\Delta x=[(x+\Delta x)+x]/\Delta x= 1\] for x>0 we get :\[f(x+\Delta x)f(x)/\Delta x=[(x+\Delta x)x]/\Delta x= 1\] so the limit of the difference quotient doesn't exist and so that the derivative at x=0

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0f(x)=x is continuous at x=0: \[f(x ^{})=\lim_{x \rightarrow 0}\left x \right=0\] \[f(x ^{+})=\lim_{x \rightarrow 0}\left x \right=0\] dw:1342611754796:dw However, \[f \prime(x)\] has a point of jump discontinuity at x=0: \[f \prime(0^{})=\lim_{x \rightarrow 0}1=1\] \[f \prime(0^{+})=\lim_{x \rightarrow 0}1=1\] dw:1342612014321:dw at x=0 left hand limit \[\neq \] righthand limit as Problem Set 1 Question 1D, 3 (d) and (e) demonstrate similar cases.
Ask your own question
Sign UpFind 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.