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.

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

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

That's really the only way to do it

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

yessss

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

I guess we have to use linear approximation to verify

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

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?

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

as in x = 1/2

Is this a calculus problem?

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

Yes, it is. I already solved it.

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

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

Phi, let me finish what I started please

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

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

What did you do?

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...

you mean 2x-4y=3

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

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

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

You will get y = x

the derivative would just be x right?

Yes

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

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

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

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

I hope that makes sense

ahhh i gotcha.. perfect sense

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

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!

:o)

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