by Tutor.com

Tweet
!function(d,s,id){var js,fjs=d.getElementsByTagName(s)[0],p=/^http:/.test(d.location)?'http':'https';
if(!d.getElementById(id)){js=d.createElement(s);js.id=id;js.src=p+'://platform.twitter.com/widgets.js';
fjs.parentNode.insertBefore(js,fjs);}}(document, 'script', 'twitter-wjs');

System Message

[00:00:00] *** Please note: All sessions are recorded for quality control. ***

Jocelyn (Customer)

[00:00:02] HELP!

Emily L (Tutor)

[00:00:13] Welcome to Tutor.com ! How can I help you today?

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 :)

[00:09:39] please 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?

System Message

[00:11:09] *** Lost connection from Jocelyn (Customer). Waiting for reconnect... ***