Mathematics
OpenStudy (anonymous):

At what point on the graph of y=1/2x^2 is the tangent line parallel to the line 2x-4y=3? I really need help working this out.

hero (hero):

Yeah, you're going to have to use tangent line approximation for this

hero (hero):

Yes, I was on the right track before I deleted what I wrote

hero (hero):

That's really the only way to do it

hero (hero):

The first graph is $y = \frac{1}{2}x^2$ right?

OpenStudy (anonymous):

yessss

hero (hero):

Yeah, I think the answer is x = 1/2....Let me figure out a way to verify this

hero (hero):

I guess we have to use linear approximation to verify

hero (hero):

I say, use linear approximation to find the line, then check to make sure that it is indeed parallel to the given line, then make sure that the line intersect y = x^2/2

OpenStudy (anonymous):

okay you've completly lost me.. sorry... i know the answer is (1/2,1/8) im just not sure on how i got that the first time?

hero (hero):

If you noticed, I posted, "I think the answer is 1/2" earlier.

hero (hero):

as in x = 1/2

OpenStudy (phi):

Is this a calculus problem?

OpenStudy (anonymous):

i know i sound stupid but where did the y=x^2/2 come from?

hero (hero):

Yes, it is. I already solved it.

OpenStudy (phi):

If so, take the derivative dy/dx of your curve

hero (hero):

y = 1/2 x^2 is the same as x^2/2

hero (hero):

Phi, let me finish what I started please

OpenStudy (anonymous):

oh okay sorry... i didn't know that you meant it was the answer for x... okay so hang on one sec and let me get this all worked out and processed

OpenStudy (anonymous):

okay i think i got this.. maybe i'm not sure

hero (hero):

What did you do?

OpenStudy (anonymous):

ummm i'm not really sure haha... i tried to do the linear approximation and i tried to figure out how you got x=1/2...

OpenStudy (anonymous):

you mean 2x-4y=3

hero (hero):

1. Rewrite the given line in the form y = mx + b: $y = \frac{x}{2} - \frac{3}{4}$

hero (hero):

Yes, that is the line that is given, correct?

hero (hero):

2. Take the derivative of $y = \frac{x^2}{2}$

hero (hero):

You will get y = x

OpenStudy (anonymous):

the derivative would just be x right?

hero (hero):

Yes

hero (hero):

The derivative of y equals the slope, therefore.... 3. Set y' = 1/2: 1/2 = x

hero (hero):

You took the derivative of $y = \frac{x^2}{2}$ and got $y' = x$

hero (hero):

Because y prime, the derivative of y, represents the slope of y, we want to set that equal to 1/2

hero (hero):

now because y prime equals x, when we substitute y prime with 1/2, it will equal x

hero (hero):

I hope that makes sense

OpenStudy (anonymous):

ahhh i gotcha.. perfect sense

hero (hero):

Whew....the only other way to explain it would have been to write out steps using the drawing tool

OpenStudy (anonymous):

sorry i'm bad for making things complicated hahaha but you've helped me out a lot thank you. you don't know how much i appreciate it!

hero (hero):

:o)