# Tutor.com The Derivative Session

##### Apr. 19, 2012

Session Transcript - Math - Calculus, 3/17/2012 10:35PM - Tutor.comSession Date: 3/17/2012 10:35PM
Length: 22.1 minute(s)
Subject: Math - Calculus

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

Rosie (Customer)

Christopher K (Tutor)
[00:00:07] hello

Rosie (Customer)
[00:00:04] hello
[00:00:06] nice to meet yoyu

Christopher K (Tutor)
[00:00:12] welcome to tutor.com
[00:00:18] nice to meet you

Rosie (Customer)
[00:00:15] im so gadl you are hhelpignme today..again! :0

Christopher K (Tutor)
[00:00:27] no problem
[00:00:39] I am going to do the best I can
[00:00:45] shall we get started

Rosie (Customer)
[00:00:50] yes sir :)
[00:01:01] Find any critical numbers of the function. (Enter your answers as a comma-separated list.)

Christopher K (Tutor)
[00:02:09] alright i think i can help with this
[00:02:20] do you know what critical numbers are?

Rosie (Customer)
[00:02:24] yes
[00:02:32] its qhen you find the derivative, set it equal to zero

Christopher K (Tutor)
[00:02:41] perfect

Rosie (Customer)
[00:02:42] and those are the point where teh graph its the hgieghtes or the lowest

Christopher K (Tutor)
[00:02:51] right
[00:02:54] the max or min
[00:03:05] so can you take the derivative of the function for me
[00:03:41] perfect
[00:03:49] so set that equal to zero
[00:04:08] you are doing good

Rosie (Customer)
[00:04:05] do i move sin to the other side, to what?
[00:04:08] this is where i get confused

Christopher K (Tutor)
[00:04:22] yes you can do that

Rosie (Customer)
[00:05:13] ok

Christopher K (Tutor)
[00:05:36] alright i like what you are doing but wouldnt it be better to get rid of the sin
[00:05:59] if you divide both sides by sin it disappears right?

Rosie (Customer)
[00:06:01] oh so i canf actor!
[00:06:04] whyddint isee that before

Christopher K (Tutor)
[00:06:13] its alright

Rosie (Customer)
[00:06:12] thank you for makign th eproblem easier

Christopher K (Tutor)
[00:06:20] so what do you get
[00:08:13] you should have three answers

Rosie (Customer)
[00:08:45] right?

Christopher K (Tutor)
[00:08:52] okay good try
[00:08:53] almost
[00:09:05] that one is right
[00:09:39] what is cosine at 2pi/3

Rosie (Customer)
[00:09:45] ohh
[00:09:47] -1/2

Christopher K (Tutor)
[00:10:03] perfect
[00:10:08] what is that value
[00:10:41] yes

Rosie (Customer)
[00:10:43] ok
[00:10:46] and theres one more?

Christopher K (Tutor)
[00:10:56] but we also will have one where sine equals zero

Rosie (Customer)
[00:11:05] oh ok
[00:11:11] because thast the one i factored out right?

Christopher K (Tutor)
[00:11:21] because if sin is zero
[00:11:31] everything will be zero right?

Rosie (Customer)
[00:11:46] so its at 0 and pi

Christopher K (Tutor)
[00:12:02] right but is zero in our bounds?

Rosie (Customer)
[00:12:15] yes

Christopher K (Tutor)
[00:12:25] are you sure

Rosie (Customer)
[00:12:28] its from 0 to 2pi
[00:12:40] oh it has to be gretaer than
[00:12:45] not equal to got it

Christopher K (Tutor)
[00:12:51] but it doesnt include

Rosie (Customer)
[00:12:48] so its just pi then

Christopher K (Tutor)
[00:12:52] right
[00:12:54] yes
[00:13:02] so those are your three values
[00:13:05] great job

Rosie (Customer)
[00:13:17] all right
[00:13:22] got thrm right on the online hmwk :)

Christopher K (Tutor)
[00:13:33] great job

Rosie (Customer)
[00:13:33] do we ahve time for another one?

Christopher K (Tutor)
[00:13:44] yes only one more though :)

Rosie (Customer)
[00:13:47] ok no rpoblem
[00:13:51] thank you

Christopher K (Tutor)

Rosie (Customer)
[00:14:09] Locate the absolute extrema of the function on the closed interval.

Christopher K (Tutor)
[00:14:18] there's a fresh whiteboard

Rosie (Customer)
[00:14:28] thank you

Christopher K (Tutor)
[00:14:48] okay great
[00:15:05] so what do you think is the first thing you do?

Rosie (Customer)
[00:15:35] fidn the derivative

Christopher K (Tutor)
[00:15:45] great

Rosie (Customer)
[00:16:02] so we pkug all the pints in
[00:16:17] *ponts
[00:16:21] points

Christopher K (Tutor)
[00:16:26] lets graph this first it might make it easier

Rosie (Customer)
[00:16:33] ok

Christopher K (Tutor)
[00:16:41] great
[00:17:55] alright and what are the bounds we are working with?

Rosie (Customer)
[00:18:07] we are only given this

Christopher K (Tutor)
[00:18:25] yes those are our bounds
[00:18:54] so where is the max value with in the bounds

Rosie (Customer)
[00:18:50] ok

Christopher K (Tutor)
[00:19:22] do you know what the max value is
[00:19:30] i dont think so

Rosie (Customer)
[00:19:31] well, there is none
[00:19:36] becasue it keeps goign on and on

Christopher K (Tutor)
[00:19:46] okay great observation
[00:20:09] but you have to keep in mind we are only working with in the bounds of [-2,4]

Rosie (Customer)
[00:20:25] oh ok

Christopher K (Tutor)
[00:20:34] so now where is the max?

Rosie (Customer)
[00:20:37] so -2,9

Christopher K (Tutor)
[00:20:47] perfect
[00:20:52] and the min

Rosie (Customer)
[00:20:49] min is 4,3

Christopher K (Tutor)
[00:20:55] right

Rosie (Customer)
[00:21:02] ok got it
[00:21:09] well, thank you so much for your help :)

Christopher K (Tutor)
[00:21:20] great job

Rosie (Customer)
[00:21:22] thanks to you

Christopher K (Tutor)
[00:21:26] thank you for using to tutor.com

Rosie (Customer)
[00:21:29] have a good night! :)

Christopher K (Tutor)
[00:21:36] could you fill out the survey please
[00:21:38] you too

Rosie (Customer)
[00:21:41] ok
[00:21:48] no problem and i will

Christopher K (Tutor)
[00:21:53] thanks