A community for students.
Here's the question you clicked on:
 0 viewing
Rizags
 one year ago
If f is differentiable at 1, and the limit of f(1+h)/h as h>0 is 5, what is f(1)?
Rizags
 one year ago
If f is differentiable at 1, and the limit of f(1+h)/h as h>0 is 5, what is f(1)?

This Question is Closed

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1` f is differentiable at 1` so \[\Large \lim_{h\to 0}\frac{f(1+h)f(1)}{h}\] exists and it is defined based on the limit definition of the derivative

Rizags
 one year ago
Best ResponseYou've already chosen the best response.0so \[f'(1) = 5\lim_{h \rightarrow 0}\frac{f(1)}{h}\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1\[\Large \lim_{h\to 0}\frac{f(1+h)}{h}=5\] \[\Large \lim_{h\to 0}\frac{f(1+h){\LARGE \color{red}{0}}}{h}=5\] \[\Large \lim_{h\to 0}\frac{f(1+h){\LARGE \color{red}{f(1)}}}{h}=5\] so we see that \(\Large f(1) = 0\)

Rizags
 one year ago
Best ResponseYou've already chosen the best response.0so my step would be invalid?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1it's valid, I just don't see where to go with it

Rizags
 one year ago
Best ResponseYou've already chosen the best response.0oh ok. And you knew to put in that f(1) as 0 simply because the equation resembled the derivative limit?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1I saw it match up with the limit definition. Well almost match up. It was just missing the `f(1)` part

Rizags
 one year ago
Best ResponseYou've already chosen the best response.0so f(x) = 0 and f'(x) = 5?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1f ' (1) = 5 and f(1) = 0 we can't say anything about f(x) or f ' (x) in general

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1IF it was \[\Large \lim_{h\to 0}\frac{f(x+h)f(x)}{h}=5\] then we can say f ' (x) = 5
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.