Secant lines

[Lizzie]

<u>The Problem</u>:
Consider the function \(\displaystyle \L{}f(x) = 4x - x^2\) and the point \(\displaystyle \L{}P(1,3)\) on the graph of \(\displaystyle \L{}f\).
Graph \(\displaystyle \L{}f\) and the secant line passing through \(\displaystyle \L{}P(1,3)\) and \(\displaystyle \L{}Q(x,f(x))\) for x-values of 2, 1.5, and 0.5.

I need help figuring out how to find the secant line. . . This is what i had the most trouble with last time and I obviously never fully understood it.

 

[Lizzie]

Ok, I worked out the points.
(1, 3) and (2, 4)
(1, 3) and (1.5, 3.75)
(1, 3) and (.5, 1.75)
So, now that I have them, where do I go?

 

[lisasayzhi]

please delete

 

[Lizzie]

lol, i think i realized what I was doing. I graphed the original equation and then just graphed all of those points. I found the slopes of each, which are 1, 1.5, and 2.5 respectively. That's all I really needed to do, right? no hard work is really involved, lol.

 

[Lizzie]

Thanks for your help .

 

[stapel]

Welcome back! :wink:

Eliz.