Given a tangent line, find f(x)

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Homework Help Overview

The problem involves finding the function f(x) given the tangent line at a specific point and its slope. The context is calculus, focusing on derivatives and the interpretation of tangent lines.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to derive f(x) using the slope of the tangent line and the definition of the derivative. Some participants question the necessity of finding f(x) to determine f(4), while others express confusion about the derivative at that point.

Discussion Status

The discussion is ongoing, with some participants providing clarifications about the relationship between f(4) and the tangent line. There is no explicit consensus, but guidance has been offered regarding the interpretation of the problem.

Contextual Notes

Participants are navigating the implications of the problem setup, particularly regarding the values given and the definitions involved in calculus.

mbrmbrg
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I have a homework problem as follows:

If the tangent line to y = f(x) at (4,3) passes through the point (0,2), find f(4) and f'(4).

Using the slope formula and the point-slope formula, I found that the equation of the given tangent line is y = 1/4x + 2.

Now I want to find f(x) so I can actually answer the question.

I thought I might be able to solve for f(x) using the equation

f'(a)= lim [f(x+h) - f(x)]/h
h-->0

and subsituting 1/4 for f'(a), but I can't get any farther than setting that up.

help? please?
thanks!
 
Last edited:
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You don't need f(x) to know what f(4) is. You're already given f(4)
 
Thank you!
I have to remember that learning calculus does not mean forgetting the very first rules of reading ordered pairs, don't I...
 
mbrmbrg said:
Thank you!
I have to remember that learning calculus does not mean forgetting the very first rules of reading ordered pairs, don't I...
Well put! :approve:
 
what will be f'(4)?

0?
 

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