# Calculus Review - Tangent of function and find y-intercept

## Homework Statement

Consider g(ξ) = [(2H)/π] arctan(ξ).
Plot a graph of the function g(ξ).
Imagine a line that passes through the point on the curve at ξ0 = 1.30, and which is tangent to the curve at that point. Where does the tangent line intersect the vertical axis?
[DATA: H = 2.00 ; ξ0 = 1.30 .]

y=mx+b

## The Attempt at a Solution

Firstly I know that H=2 so I can easily simplify the question to (4/π)*arctan(ξ).

I then want to find the slope so I take the derivative of that function and get 4/(πξ^2+π) then plug in ξ=1.3 to find the slope at that point. The result is: 0.473323

I can also plug ξ=1.3 in to the original equation to find the y value at that point. The result is: 1.16514

Plugging in those values to y=mx+b I get 1.16514=(.473323)(1.3)+b. The resulting y-intercept (b) is 1.89.

Unfortunately, this is not correct! I am obviously making a silly mistake somewhere. Is anyone able to point out what I did wrong?

Thank you!

SteamKing
Staff Emeritus
Homework Helper
You didn't evaluate y = mx + b correctly.

If y = 1.16514 and mx = 0.473323*1.3, then b must be less than 1.16514

I really have no idea what to say. I'll start with a thank you. Sometimes the most obvious things...

SteamKing
Staff Emeritus