Given a tangent line, find f(x)

In summary, the conversation discusses finding the value of f(4) and f'(4) given certain information about the tangent line of y = f(x) at the point (4,3). The equation of the tangent line is determined to be y = 1/4x + 2 and it is realized that f(x) is not needed to find f(4). The conversation concludes by acknowledging the importance of remembering basic math principles in calculus.
  • #1
mbrmbrg
496
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:
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  • #2
You don't need f(x) to know what f(4) is. You're already given f(4)
 
  • #3
Thank you!
I have to remember that learning calculus does not mean forgetting the very first rules of reading ordered pairs, don't I...
 
  • #4
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:
 
  • #5
what will be f'(4)?

0?
 

What does it mean to find f(x) given a tangent line?

Finding f(x) given a tangent line means to determine the equation of the function that the tangent line touches at a specific point. The tangent line represents the slope of the function at that point, and by finding f(x), we can determine the value of the function at that point.

Why is it important to be able to find f(x) given a tangent line?

Being able to find f(x) given a tangent line is important in many applications of mathematics and science. It allows us to determine the behavior of a function at a specific point, which can be useful in areas such as optimization, physics, and engineering.

What information do I need to find f(x) given a tangent line?

To find f(x) given a tangent line, you will need the coordinates of the point where the tangent line touches the function, as well as the slope of the tangent line at that point. This information can be obtained from the equation of the tangent line or from a graph.

What are the steps to find f(x) given a tangent line?

The steps to find f(x) given a tangent line are:
1. Identify the coordinates of the point where the tangent line touches the function.
2. Determine the slope of the tangent line at that point.
3. Use the slope-point form of the equation of a line to write the equation of the tangent line.
4. Set the equation of the tangent line equal to f(x) and solve for x to find the x-coordinate of the point of tangency.
5. Substitute the x-coordinate into the original function to find the corresponding y-coordinate.
6. Write the equation of the function with the found point and slope.

What are some common mistakes to avoid when finding f(x) given a tangent line?

Some common mistakes to avoid when finding f(x) given a tangent line include:
- Forgetting to set the equation of the tangent line equal to f(x) to solve for x.
- Making a calculation error when finding the slope or solving for x.
- Using the wrong coordinates for the point of tangency.
- Not checking the final equation of the function to ensure it satisfies the given tangent line.
- Forgetting to include the point of tangency in the final equation of the function.

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