calculus

[Jon]

Hey guys. I'm hoping some of you know something about Calculus. I'm having some problems in the class and I really can't understand this problem. Maybe someone could help me out and try to explain it. Here it is:

given: the function y=f(x) is defined by f(x)=x^2
The point (c,d) is an arbitrarty point in the xy-plane.
The line tangent to y=f(x) at the point (x1,y1) passes through (c,d)

question: If c=0 and d=1, do you think (x1,y1) exists? Prove your assertion. Hint: assume (x1, y1) exists, and try to find (x1,y1).

Please help me on this if you have any kind of idea. Thanks.

[ohsix]

you might have better luck in boats and accesories. there's some smart dudes in there. also you might try bringing it to OttoNP's attention. he's usually pretty smart

[FRANKIE]

i took calc I and II back like 4 years ago... so i'm a little rusty. think about what it means to have a line tangent to a point = this is the first derivative of that point/value (of the equation that that line defines).

i am like wise studying for an exam right now... i just thought i would throw that hint out (maybe you've already thougth about it?) and i'll try to take a look at this later.

remember calc isn't easy... you gots to be patient!
good luck!
frankie

p.s. my daddy's a mathematician... so if anything i'll throw the problem his way later tonight and hopefully we can help you out, buddy.

[Jon]

thanks for the replies. I've thought about it for a while and I've got this as an answer, maybe someone could check me on it.

No, the point (x1,y1) would not exist. The line tangent to f(x)=x^2 that goes through the point (c,d) would not be a tangent line to any part of the function. It would pass through f(x) more than once or be a vertical line which would not be a tangent line. The line tangent to the function is unique in that it is only the tangent line to one point on the function.

[project3060]

No- The function X^2 is a parabola that has a vertex at the orgin (0,0). The tangent of the parabola at any point (x1, y1) will have zero or negative y- intercept point. The point c=0, d=1 is a point with a positive y value and therefore can not be a point along any tangent of X^2

[OttoNP]

Proofs really suck, I've always hated them, but maybe this will help...

Basically what you are doing is trying to see if you can connect a line from (0,1) to a point that lies on f(x)=x^2 and have it be tangent as well. In order to be tangent, the slope of that line must be equal to the derivative of the function at that point:

Let's start with an example with actual points, this sometimes help you see what your looking for, pick a point on f(x)=x^2, say (2,4). Now, you can make a line that goes from (0,1) to (2,4), it will have a slope of (4-1)/(2-0)=3/2. The derivitive of f(x)=x^2 is 2*x, so the slope of f(x) at (2,4) is 4, since the slopes aren't equal, this point does not satisfy the condition.

Below is where your "proof" would start
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Now you need to check for all points on the function. Any point on f(x) will be (x,x^2) since f(x)=x^2, meaning y=x^2. The slope of a line from (0,1) to that point will then be (x^2-1)/(x-0). This slope needs to be the same as f'(x), which is f'(x)=2*x, so what must happen is (x^2-1)/(x-0)=2*x, changing this around is x^2-1=2*x^2, then -1=x^2 and finally you get x=sqrt(-1), which would mean x=i. Since i is not a real number, it's on the complex plan, the condition can't be satisfied. If you look at a plot of f(x)=x^2 and the point (0,1), you can see that it is unlikely that a line from that point would ever be tangent to f(x), but you can see with other points it could happen.
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As an example, let's say c=0 and d=-4 instead, so the point your checking for now is (0,-4). Following the same process, the slope would then be (x^2+4)/x, setting this equal to the derivative and solving you get, (x^2+4)/x=2*x, which is x^2+4=2*x^2, which is x^2=4 and x=2. So the point on f(x) is (2,4), this checks since a line from (0,-4) to (2,4) has a slope of 4 and the derivative of f(x) at (2,4) is also 4. Looking at a plot of f(x) and (0,-4) you can see that a line can be formed that is tangent.

Hope this helps,
Nick
________
Lincoln navigator picture

[Jen]

is calculus at college hard? i'm still in high school but i'm taking a class at the university next year and i'm thinking it'll be too hard.

[Grouch]

[b]Take the square root of the equilibrium and multiply it by the flux capicator and you should get your answer

[OttoNP]

Jen,

A lot of it will depend on what school you go to, but it probably won't be any harder than your high school class, it will probably start as review and then go past what you learned. They always try to scare you, when your in elementary school they say you'll die in junior high, when your in junior high they say you'll die in high school, etc... Engineering schools will probably be harder than non-engineering. I went to Georgia Tech and had to take Calc. 1-4, an easier linear algebra class, and differential equations before I graduated. I would say the majority of students felt calc 4 was a little tough, and differential equations can blow with the wrong teacher. If your not going into engineering you probably won't take much.

Nick
________
Vapir No2

[TSHutch]

I was gonna help.
But Otto beat me to it.
Hes the man listen to him.

[BR_WB]

Yea I'm not good at math, but I think I remember something about that.

[FRANKIE]

jen.
i took calc I and II at the uni when i was a junior in high school (did i mention my dad was a mathematician? ha ha). any way, the big difference is that you actually have to study for the class daily. you can't just slack off and start studying for an exam 3 days ahead of time or even worse the of (that's what i did for all of my other high school classes and i still got A's. you won't get A's in college using that method though). you'll be fine... just do it to it!

take care.
frankie

[Jen]

thanx guys, i'll come runnin to y'all if i have any problems

[Aubs]

i have to take calc senior year - YUCK

[Jello John]

[Chukee_R]

Smart people....YAY FOR INTRO TO COLLEGE ALGEBRA!

[ohsix]

hell yeah chukee. college algebra for the second time right here. going to class helps, especially on test days.
my advisor was a little disturbed that my major is mechanical engineering and i dropped college algebra last semester.

[Nor*Cal]

I took calc 3 times my first 2 years of college. I finally passed with a C. I withdrew the first 2 tries.

[NatalieShay]

yeah Jen, be prepared to form a study group the first day of school!! Im taking business calculus at UT and its really really really hard! I have a B in there right now...just as long as you study every night and dont miss any class, you can keep up

[JHrod]

ur all wrong--the correct answer is E=M.C. Hammer^2

[Jen]

thanx guys i'll keep all this in mind when i'm failing

[Chales]

I got a 5 on the AP Calc Test Sophomore year in high school.

[JHrod]

chales---r u a computer with a whitty human-like personality??????

[grady]

yo aubs...rite there w/ ya on that one. just got outta precal last semester...it wont too bad. dreadin next year when ap calculus comes along

[JHrod]

so aubs---how hard is that algebra 2 shiz???

[Jello John]

[Chales]

Just like anything else, if you work hard at it and study you'll get a good grade. But I'm pretty sure that you can't take both AB and BC in the same year.

[Chales]

Ya, here, check this:

http://www.collegeboard.com/ap/students/exam/choice.html

[Jello John]

That sucks! Ok, I guess I'll take the BC test next year even though I have the class right now. I'm going to try Calc III next year anyways so I don't think it will matter too much.

Have you taken any other AP tests? So far I've only taken the US History test and I got a 4 on it.

[Chales]

No, just calc. I'm a junior now, and I'm taking Bio, Calc 2, and History this year. Is US History hard? Because it's definately a hard class to get through. Its so hard to remember all the details of the past 300 years.

[ohsix]

AB, BC??? nothin smaller than C's right here. D's are nice but DD's can be too big sometimes.

[Breezer]

go to www.hotmath.org

That site will have solutions to most high school math books. With some hints.

[Jello John]

[Chales]

How can you manage to take all those tests? Are you homeschooled or something?

[Jello John]

No, I go to a public school. I don't know, I probably won't study a whole lot for them. I have three of the four classes for those AP tests right now which should help a lot. My nights are pretty busy though.