Another Tangent Line Question

[Scrutinize]

Yea but when I solve that equation I get the wrong answer? I got 1+ 21^(1/2) divided by two and the same but minus. And when I plugged the equation into a calculator it gave that answer too, which was wrong. Is there a small mistake that we're making maybe?

[MATH]0=\frac{4a+1}{(a^2-1)^{\frac{3}{2}}}(a+1)+\frac{a+4}{\sqrt{a^2-1}}[/MATH]
This is the exact equation I am using.

 

[Dr.Peterson]

Yea but when I solve that equation I get the wrong answer? I got 1+ 21^(1/2) divided by two and the same but minus. And when I plugged the equation into a calculator it gave that answer too, which was wrong. Is there a small mistake that we're making maybe?

[MATH]0=\frac{4a+1}{(a^2-1)^{\frac{3}{2}}}(a+1)+\frac{a+4}{\sqrt{a^2-1}}[/MATH]
This is the exact equation I am using.

This is from solving the equation you stated before, a^3 - 6a -5 = 0 ? Please show how you obtained that. Also, how do you "know" that your answer is wrong? I'm not sure what you are saying there.

 

[Scrutinize]

Gyazo

gyazo.com

-1 isn't in the domain so it isn't an answer and then those are the two answers for a. When you plug those into the derivative (because a is the x-value of where the tan line would hit (0,-1), and the goal of the problem was to find the slope of the tan line) the answer is not correct, at least it isn't the same value that it shows on the answer key nor what was put in this thread earlier, so either the other answers were wrong or we made a slight mistake here, but I'm not sure exactly.

Do you get what I'm saying? Thanks by the way.

 

[Dr.Peterson]

Gyazo

gyazo.com

-1 isn't in the domain so it isn't an answer and then those are the two answers for a. When you plug those into the derivative (because a is the x-value of where the tan line would hit (0,-1), and the goal of the problem was to find the slope of the tan line) the answer is not correct, at least it isn't the same value that it shows on the answer key nor what was put in this thread earlier, so either the other answers were wrong or we made a slight mistake here, but I'm not sure exactly.

Thank you for saying why you think your answer is wrong; but you ought to have told us what the answer key says, in case it is wrong! (It's a good idea to do so from the very beginning, as that sometimes prevents what would be a long wasted discussion if it turns out you were right all along.)

I see the answer was given in post #10; are you saying that is, or isn't, what the answer key says? It is also what I get.

But you haven't done the other thing I asked for, which is the steps in your work. I suspect a sign error, but I can't tell without seeing how you got your cubic equation. My guess is that in showing us that work, you will catch your own error.

By the way, why can't you attach an image directly rather than linking to gyazo? It's a lot easier to read.

 

[Scrutinize]

Yes I did notice I wrote the sign down incorrectly on my paper and that is why I was getting it wrong. It's dumb mistakes like these that i always end up being subject to.


Separate question because this always happens to me on exams, do you have any advice on how to stop making stupid mistakes. I make really simple mistakes a lot of the time and I'd prefer to reduce that on the test. I usually understand the concepts but what ends up hurting me are simple mistakes that screw me over. Is there anything you know that I could do that would help reduce the amount of stupid mistakes I make? Thank you very much!

 

[Dr.Peterson]

Separate question because this always happens to me on exams, do you have any advice on how to stop making stupid mistakes. I make really simple mistakes a lot of the time and I'd prefer to reduce that on the test. I usually understand the concepts but what ends up hurting me are simple mistakes that screw me over. Is there anything you know that I could do that would help reduce the amount of stupid mistakes I make?

1. Slow down.
2. Write more steps than you think you have to. You don't see mistakes that are floating around in your head.
3. Check each step you write by comparing to the line above and asking yourself why each change occurred.
4. Also, when you make a mistake doing practice problems, don't move on until you've pondered why it happened and how you could have prevented it. It might be something simple like "I wrote unclearly and misread that sign", or something big like "I wrongly assumed it was this other kind of problem". Make a mental checklist of things to avoid.

Here is a post on my blog about this very topic, in which I summarized what three of my colleagues have written about it. The links to their full answers are worth following, because I omitted a lot of detail.