# Thread: Function, secants and tangents

1. ## Function, secants and tangents

f(x) = -2/(x-7)

We will take steps to find the tangent line to the graph of f at the point (42/3)

(a) Let
(xf(x)) be a point on the graph of f with x=4. The slope of the (secant) line joining the two points (42/3) and (xf(x)) can be simplified to the form a/(x-7) where A is a constant. Find A .

(b) By considering the slope of the secant line as x approaches 4 , find the slope of the tangent line to the graph of f at the point (42/3)

(c) Find the equation of the tangent line to the graph of f at the point (42/3). Write your answer in the form y=mx+b.

No clue how to find A, first of all. I'm struggling with the rest obviously too or I wouldnt have posted it, but I'm trying to go one step at a time here. If you can help with all of it, that's great too though.

2. Judging from this problem, do you happen to go to university in Calgary?

Hehe, anyways.... I missed a class (snow), so hopefully I'm close to the proper method.

(a)Anyhow, it's asking for slope, so
$\displaystyle \frac{y_2-y_1}{x_2-x_1}$. Here, lets put $\displaystyle y_2=\frac{-2 }{(x-7)}$ and $\displaystyle x_2=x, y_1=\frac{2}{3}$ $\displaystyle , x_1=4$

So, after this, I would get rid of the fraction in the top, and simplify enough to get the form they are asking for. Should work out perfect. And as for the rest, if you think of it with the slope idea, it should come naturally to you.

(b) Using the equation you got from the last part, solve the limit as x approaches 4 for it.
(c) Substitute the slope, an x value, and a y value in and solve for b. That will give you your equation. (the y and x value are given, the slope you calculated)

And if anyone else sees something wrong with my methods or work, feel free to correct.

Good Luck!