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Exactly

I recognize now that I read the solution too fast. In other words, I misread it. Speed reading, if it works anywhere (highly debatable) , doesn't in mathematics.

Yes, I see that now. I have misread the solution . This sometimes happens to me. I misread something and from then on that misreading undermines the whole enterprise.

I am sorry that I posted that second image--it was completely wrong. What happened is that I had worked out the tangent equation a couple of times but it was so messy that I quickly rewrote it so that it would look more presentable and in the process left out steps and made a complete hash of...

The following is a (small) portion of a solution from a solutions manual keyed to a much renowned calculus text--author James Stewart. The whole problem is complex and not really relevant to report here. What I want to know is: How is this tangent equation being derived. I can't for the life of...

Yes. I started thinking about your post at three in the morning--it doesn't cure insomnia but puts it to some use anyway--and in a flash saw the light! What I had been doing was using the right coordinates with the wrong slope. Exactly what I was thinking about when I did that I'm not...

Right. After I found a and b I found c by plugging 1 into the equation of the parabola and setting y to 4. Working this out I got 0 for c.

Thanks for the reply. I will have to ponder what you are saying here. I don't see clearly what you are getting at but I have a vague sense of it. I will work on this again tomorrow keeping in mind this post and get back here with my results.

Here is the problem I am working with: In the process of solving or trying to solve this I looked at the solutions manual and understood that they way to go was with a system of equations. I then found the the function asked for. Then, I wanted to find the linear functions of the tangents so I...

Sorry, the work was sloppy. I will go at it again today and also take a photo of the problem. In the problem it was stated what the slope was at two values of x. I may have mixed things up somehow. I will work this all out again today and post results. Thanks very much for pointing out the...

Thanks for your reply. I am going to work on this again today to make sure I used the right value. I will also take a photo of the problem and post it.

This is the solution to a problem that asked the student to find a function of the form ax^2 +bx+c given certain information relating to the slopes at certain values of x. Also a set of coordinates was given . Anyway, I worked out the problem and managed with the help of the solutions manual (I...

Right. I should have put an h there in as much as it is as yet unknown, at least it hasn't been given in the problem's description.

I worked on this matter again yesterday. I went through the thing in pretty much the same way the author does. I used the information given in the problem: We are given that when the light is closest to the path along which the man is walking it is 20 feet from it. and we are asked , if said...

Thanks for the comment. I will think about what you have said.

Yes, I see that I lost track of that dy/dt. That should have been in there somewhere...I am confused here as to how implicit differentiation is to be accounted for here. I have to go back and go over that again. Then thee is the business of y=20. I will go over this stuff again today an d try to...

So, once again I went at it today, this time with better understanding and higher hopes. I Think I understand now why Dr. Stewart used the tangent instead of the sine function. As Dr. Peterson explained, the tangent (sine/cosine) is the function that allows all the information given in the...

Thanks for your reply. I will have to wait til the morning to digest it--my brain shuts down after 10PM these days. I will get back with my results tomorrow.

Well, I went at it again today with this, keeping in mind that there are certain dynamisms in this business of related rates that have to be kept in mind. But I soon found myself walking in darkness again. Here is what I did: I first found the derivative formula and then plugged in the values...

I see that you are right. I have to go back and rethink this whole matter of related rates. Yes, absolutely, some of those parameters are dynamic. I was not thinking the thing through. Thanks.