Help with a Math Problem...

[Moto]

Hey Halflife2.net.

I'm having trouble getting the correct answer for this calculus problem. Or maybe my book is giving me an incorrect answer in the back, I'm not sure.

Here it is. Check it out and see if you get the same answers I'm getting.

My work:

The back of my book says these are the answers:

(A) -3; slope of the secant line through (1, f(1)) and (2, f(2)).

So I got this one right.

(B) -2-h; slope of the secant line through (1,f(1)) and (1+h, f(1+h)).

I have no idea how they got this answer. I get 2+h every time.

(C) -2; slope of the tangent line at (1, f(1)).

Obviously, if (B) is wrong, (C) will be wrong too. So, since my answer in part (B) is 2+h, my answer in part (C) will be 2 instead of the book's answer of -2.

Any math people here who can spot my error or confirm that the book has a typo?

Thanks for any help.

Pat

 

[Jintor]

Hmmm.

In b, when it says

5 - 1 + 2h + h^2 - 4/h

It should be 5 - (1 + 2h + h^2) - 4 / h

Common mistake.

Dunno if that'll solve your problem, but that's what jumps out at me.

/EDIT yeah, that makes (b) = -2 - h. Checking part c...

Yep. That was the mistake.

Let me write it up for you.

 

[Moto]

Hmmm.

In b, when it says

5 - 1 + 2h + h^2 - 4/h

It should be 5 - (1 + 2h + h^2) - 4 / h

Common mistake.

Dunno if that'll solve your problem, but that's what jumps out at me.

Well no, you can remove the parenthesis since everything has been multiplied out. After you've removed them, you subtract 1 from 5 and you get 4. Since there is a -4 on the other side, you can cancel them out since 4-4=0. So then you're left with (2h+h^2) / h.

EDIT: But yeah show me what you did. I could very well be wrong.

 

[Jintor]

Well since I get the correct answer if I do what I did, I'm inclined to believe it goes my way. Anyway take a peek at the working.

And you don't remove the parenthesis once everything is multiplied out, because it's still "5 - (1+h)^2" = 5 - (1 + 2h + h^2) = 5 - 1 - 2h - h^2.

See?

 

[mindless_moder]

in b when you expand (1+h)^2 you need to multiply in the negative , so you get

> (5-1 - 2h - h^2 -4) / h
> (4 - 4 - 2h-h^2) / h
> (-2h-h^2) /h
> h(-2-h) /h
> -2-h

edit: don't you just hate first principles ? .

 

[Moto]

Well since I get the correct answer if I do what I did, I'm inclined to believe it goes my way. Anyway take a peek at the working.

And you don't remove the parenthesis once everything is multiplied out, because it's still "5 - (1+h)^2" = 5 - (1 + 2h + h^2) = 5 - 1 - 2h - h^2.

See?

I see what you did. Sorry, I didn't mean to doubt you, its just that my instructor has done what I did in a similar situation and it worked out. I don't know, I get this unwarranted sense of confidence in my working of certain problems and I doubt the book's answer at times, so forgive me for sounding arrogant. No disrespect to you.

Thank you so much for your help! I really appreciate it, bud.

Pat.

 

[Jintor]

No worries. Just remember that you don't collapse the paranthesis immediantly once you've expanded it out.

Hmmm. I sense another maths thread coming up!

Did you photograph your book or scan it? Or is it a PDF you screengrabbed?

 

[mindless_moder]

I'm not sure about what level you're learning at but later on you're going to learn how to do these problems in single steps. Nobody actually uses first principles to calculate derivatives, they're mostly just used to introduce the concept or in proofs.

 

[Moto]

No worries. Just remember that you don't collapse the paranthesis immediantly once you've expanded it out.

Hmmm. I sense another maths thread coming up!

Did you photograph your book or scan it? Or is it a PDF you screengrabbed?

Thanks, man. I scanned it.

I'm not sure about what level you're learning at but later on you're going to learn how to do these problems in single steps. Nobody actually uses first principles to calculate derivatives, they're mostly just used to introduce the concept or in proofs.

This is my first calculus class and we just covered the "long way" of doing derivatives on Wednesday. When I go back on Monday, she is teaching us the "short way." She said she wanted us to learn this first.

 

[Jintor]

You still need to know differentiation from first principles.