Hey guys, I've been having my butt kicked after coming back to school from a 8ish year hiatus. I'm in calculus now and trying to keep up but the word problems are beating me up.

I was given a take home test (to save me, somehow) and have a couple questions. I'm not necessarily looking for someone to do everything for me, but I would at least like some advice/direction.


The first question I have:

According to an article, SAT scores are declining at a slower rate. Interpret this statement in terms of a function and its first and second derivatives.

^ I'm not sure what function to use for this, as we never really went over anything like this in class. The interwebs has given me a few but I don't want to use something we never learned in class (I think he wants us to stick to that).


Thank you!

/e Lol that spelling error in the title D: *derivatives.

/e2 the teacher sent an attachment that updated what he wants but it didn't help me:

consider Homer's statement. Pretend there is a function f(t), where t is time. What is the function? What do you know about it's first and second derivatives at that moment in time?

This post was edited by 1hitko2 on Mar 12 2016 06:16pm

You don't need an actual function.

SAT scores are declining --> Implies that the first derivative is negative.

The rate at which they are declining is decreasing --> Implies that the second derivative is positive. This one may be less intuitive. At first they are declining quickly, so the first derivative at t = x is "very negative", but they stop declining as quickly as time goes on, so the first derivative at t = X + Y is "less negative". The first derivative graph is increasing, so the second derivative is positive.

If you really want to, you can just model the sat scores as something like

Score(t) = 2000 - 100sqrt(t)


This post was edited by RzChaos on Mar 12 2016 07:14pm

Ok good, I was thinkin that but wasn't 100% sure. Thank you a ton for the help!