You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an alternative browser.
You should upgrade or use an alternative browser.
Prove from the definiton of differentiability that the function
- Thread starter K80dol
- Start date
Why is this in algebra?f(x)= (2x-1)/(x-2) is differentiable at 1, andfind f ' (1).
Please any help with this question woud be fantastic! I understand that the quotient theory goes something like
Q(h) = (f(x +h) -f(x))/h
That is not the quotient theorem.
In any case, the problem asks you to prove this using the definition of the derivative so you cannot use the quotient theorem.
What is the definition of the derivative?
What is f(x + h) in this case?
Prove from the definiton of differentiability that the function
f(x)= (2x-1)/(x-2) is differentiable at 1, andfind f ' (1).
Please any help with this question woud be fantastic! I understand that the quotient theory goes something like
Q(h) = (f(x +h) -f(x))/h or am i completely wrong?
Please any help with this question woud be fantastic! I understand that the quotient theory goes something like
Q(h) = (f(x +h) -f(x))/h or am i completely wrong?
If you take the limit as h-->0 of the formula you called Q(h), then you will have the definition of "derivative".f(x)= (2x-1)/(x-2) is differentiable at 1, and find f ' (1).
Please any help with this question woud be fantastic! I understand that the quotient theory goes something like
Q(h) = (f(x+h) -f(x))/h
\(\displaystyle \displaystyle f'(x) = lim_{h\to 0} \left[ \dfrac{f(x+h) - f(x)}{h} \right]\)
From the point of view of "algebra", evaluate your f(x) function at x=(1+h) and at x=1, subtract, divide by h, and take the limit. If you need more help, please show us your work.
Double post.Prove from the definiton of differentiability that the functionf(x)= (2x-1)/(x-2) is differentiable at 1, andfind f ' (1).
Please any help with this question woud be fantastic! I understand that the quotient theory goes something like
Q(h) = (f(x +h) -f(x))/h or am i completely wrong?
I was advised that my previous question was in the wrong category, so have moved it. I thought this forum was called freemathHELP, not one word useless answers. Sorry i am new to this forum and may not know the correct way to post, but help woul be appreciated.
It helps us and you if you read Read Before Posting before posting.I was advised that my previous question was in the wrong category, so have moved it. I thought this forum was called freemathHELP, not one word useless answers. Sorry i am new to this forum and may not know the correct way to post, but help woul be appreciated.
One thing that helps us help you is to know where you are in your math education. Are you just starting calculus? Are you in college? Is this self-study? Hard to help YOU if we know nothing about you.
You have been told that your Q(h) is not the quotient theorem.
As Dr. Phil already told you, the definition of the derivative is \(\displaystyle f'(x) = \displaystyle \lim_{h \rightarrow 0}\dfrac{f(x + h) - f(x)}{h}.\)
Dr. Phil also told you how to attack this problem.
What is f(1 + h)? What is f(1)? So what is f(1 + h) - f(1)? What do you get when you divide that difference by h? What do you get when you take the limit of that quotient as h approaches 0? Show us your answers to those four questions, and we can tell you whether you have made a mistake and if so where. If you cannot answer all four questions, answer those that you can. If you cannot answer any of them, you are not ready for calculus.
Last edited:
HallsofIvy
Elite Member
- Joined
- Jan 27, 2012
- Messages
- 7,763
I see no one word answers, and certainly no "one word useless answers".I was advised that my previous question was in the wrong category, so have moved it. I thought this forum was called freemathHELP, not one word useless answers. Sorry i am new to this forum and may not know the correct way to post, but help woul be appreciated.
Perhaps the problem is your misunderstanding of the word "help". Doing a problem for you is not helping. You have been told what you need to do to answer this question. If you are not clear on how to do that, show what you have tried and we can try to point out errors and give hints.