# Tutor.com The Derivative Session

##### Jan. 3, 2014

Session Transcript - Math - Calculus, 1/2/2014 7:50PM - Tutor.comSession Date: 1/2/2014 7:50PM
Length: 11.2 minute(s)
Subject: Math - Calculus

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Jocelyn (Customer)
[00:00:02] HELP!

Emily L (Tutor)

Jocelyn (Customer)
[00:00:45] URL > http://jupiterserve.com/teacher/929647/21_Holiday_Take_Home.pdf
[00:00:54] hello :)
[00:01:13] I need help on the first 6 problems :)

Emily L (Tutor)
[00:01:35] ok, we probably won't be able to get to all six, but let's go ahead and get started

Jocelyn (Customer)
[00:01:45] okay that's great :)

Emily L (Tutor)
[00:02:17] do you want to go in order?

Jocelyn (Customer)
[00:02:30] yeah

Emily L (Tutor)
[00:02:58] ok, then let's start with the first one. where are you stuck in this problem?

Jocelyn (Customer)
[00:04:13] i don't understand how to do this without a calculator

Emily L (Tutor)
[00:04:41] ok! do you know what it means for a function to be concave up? in terms of derivatives, not just what the graph looks like

Jocelyn (Customer)
[00:05:48] yes the first derivative has to be positive :)

Emily L (Tutor)
[00:06:01] almost! it's the second derivative for concavity
[00:06:51] but the same general idea :) so the function is (x^2+1)/(x^2). do you see any ways to simplify before we take derivatives? i always like to do that first in case it makes derivatives easier

Jocelyn (Customer)
[00:07:16] so the second derivative has to be positive?

Emily L (Tutor)
[00:07:22] correct

Jocelyn (Customer)
[00:08:16] how would we simplify?

Emily L (Tutor)
[00:08:42] well, think back to algebra and splitting fractions. let me write something on the white board

Jocelyn (Customer)
[00:09:05] i thought we would use quotient rule?

Emily L (Tutor)
[00:09:10] well we can

Jocelyn (Customer)
[00:09:20] ohhhh okay go on

Emily L (Tutor)
[00:09:25] but sometimes you can simplify the function to avoid having to use the quotient rule!

Jocelyn (Customer)
[00:09:34] oh okay go on :)

Emily L (Tutor)
[00:09:48] ok, so in our case, we have something that looks like this:
[00:10:26] hang on, before i do this, have you learned how to take derivatives of functions to a negative power?
[00:10:32] like... x^(-4)

Jocelyn (Customer)
[00:10:38] yes :)

Emily L (Tutor)
[00:10:41] ok great!
[00:11:01] so do you see how this will simplify?

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