Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
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)...
 one year ago
 one year 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)...
 one year ago
 one year ago

This Question is Open

iisthphirBest ResponseYou've already chosen the best response.1
The 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.
 one year ago

khoutirBest ResponseYou've already chosen the best response.0
the 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
 one year ago

JingleBellsBest ResponseYou've already chosen the best response.0
f(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.
 one year ago
See more questions >>>
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.