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.

Question

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 · Answer

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

hero · Answer

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

hero · Answer

That's really the only way to do it

hero · Answer

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

anonymous · Answer

yessss

hero · Answer

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

hero · Answer

I guess we have to use linear approximation to verify

hero · Answer

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

anonymous · Answer

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 · Answer

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

hero · Answer

as in x = 1/2

phi · Answer

Is this a calculus problem?

anonymous · Answer

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

hero · Answer

Yes, it is. I already solved it.

phi · Answer

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

hero · Answer

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

hero · Answer

Phi, let me finish what I started please

anonymous · Answer

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

anonymous · Answer

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

hero · Answer

What did you do?

anonymous · Answer

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...

anonymous · Answer

you mean 2x-4y=3

hero · Answer

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

hero · Answer

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

hero · Answer

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

hero · Answer

You will get y = x

anonymous · Answer

the derivative would just be x right?

hero · Answer

Yes

hero · Answer

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

hero · Answer

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

hero · Answer

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

hero · Answer

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

hero · Answer

I hope that makes sense

anonymous · Answer

ahhh i gotcha.. perfect sense

hero · Answer

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

anonymous · Answer

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 · Answer

:o)