Given a tangent line, find f(x)

Click For Summary
The discussion revolves around a calculus problem involving a tangent line to the function y = f(x) at the point (4,3) that passes through (0,2). The user correctly identifies the slope of the tangent line as 1/4 and seeks to find f(x) and f'(4). It is clarified that f(4) is already known as 3, based on the given point. The conversation highlights the importance of understanding ordered pairs in relation to calculus concepts. Ultimately, the user is reminded that f'(4) is equal to the slope of the tangent line, which is 1/4.
mbrmbrg
Messages
485
Reaction score
2
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:
Physics news on Phys.org
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?
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?
View full post »

Similar threads

Can a Function Have Two Different Tangent Lines at the Same Point?
  • · Replies 2 ·
Replies
2
Views
1K
How can I overcome the lack of support for my passion for mathematics?
  • · Replies 15 ·
Replies
15
Views
2K
Find the two points on the curve that share a tangent line
  • · Replies 9 ·
Replies
9
Views
2K
Can you clarify your understanding for parts (a) and (b)?
  • · Replies 11 ·
Replies
11
Views
2K
Find the slope of the tangent line to the function's inverse
  • · Replies 13 ·
Replies
13
Views
4K
Lagrange multipliers understanding
  • · Replies 8 ·
Replies
8
Views
2K
Calculating the equations for the tangent/normal lines
  • · Replies 5 ·
Replies
5
Views
2K
Find the equation of the tangent plane and normal to a surface
  • · Replies 1 ·
Replies
1
Views
1K
Quadratics Having a Common Tangent
  • · Replies 1 ·
Replies
1
Views
998
How to find the straight tangent line?
  • · Replies 6 ·
Replies
6
Views
1K