Expert: Paul Klarreich - 10/5/2010

Question
What is the formula for the line intersecting the graph of f at x=1 and x=3, where f(x)= 10/xsq.+1?  If I solve for f(1) I get 5 and f(3) I get 1 but I don't know how to proceed.

Answer
Questioner:   JoAnn
Country:  United States
Category:  Calculus
Private:  No
 
Subject:  Formula for a lline intersecting
Question:  What is the formula for the line intersecting the graph of f at x=1 and x=3, where f(x)= 10/xsq.+1?  If I solve for f(1) I get 5 and f(3) I get 1 but I don't know how to proceed.
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Now that you have discovered the two points of intersection:

x1 = 1,  y1 = 5   and
x2 = 3,  y2 = 1

use these two points to:

A. Determine the slope of the line.
B. Use that and either point in the point-slope form:

y - y1[or y2] = m(x - x1[or x2])

and you'll have it.


Note: Next time you send a question, please read my instructions.  You were careless in writing your function.  You meant to write:
         10
f(x) = --------
      x^2 + 1

But you actually wrote:

      10
f(x) = ---  + 1
      x^2

which is not the same.