User:PseudonympH
Just to clarify, it's actually Pseudonym-pH. I tacked the pH on when regular "Pseudonym" was taken on Battle.net because it's, well, a science term. I also thought it was cool that it flowed well like that, so I kept the suffix. And no, as some people might think, I am not a female. :P
Math Class
If you're here because of the link posted on Nicenet, here's where you can find the nifty formulas and stuff. I did it here instead of there because i can do pretty math formatting like this:
Midyear review, number 11.
(Because it was the only one left :) )
For the function
a. Find the equation of the tangent line to the graph of f(x) at (1,2).
First, we start off by finding the derivative of f(x)
Taking this when will give us m for our y=mx+b equation. We can therefore conclude that m=3, and we can them solve for b:
The equation of the tangent line is then y=3x-1.
b. Prove that f(x) is equal to 3 somewhere in the interval [1,2].
We can prove this easily using the Intermediate Value Theorem. First evaluate when x=1:
Then evalute when x=2:
Here we hit a bit of a snag, as we can't (easily) evaluate ln(2). However, since 2 is less than e, ln(2) must be less than 1. Therefore,
By the Intermediate Value Theorem, we can conclude that there is a number k on [1,2] such that f(k)=3.