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.

Answer 1

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

Answer 2

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

Answer 3

That's really the only way to do it

Answer 4

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

Answer 5

yessss

Answer 6

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

Answer 7

I guess we have to use linear approximation to verify

Answer 8

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

Answer 9

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?

Answer 10

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

Answer 11

as in x = 1/2

Answer 12

Is this a calculus problem?

Answer 13

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

Answer 14

Yes, it is. I already solved it.

Answer 15

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

Answer 16

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

Answer 17

Phi, let me finish what I started please

Answer 18

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

Answer 19

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

Answer 20

What did you do?

Answer 21

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...

Answer 22

you mean 2x-4y=3

Answer 23

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

Answer 24

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

Answer 25

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

Answer 26

You will get y = x

Answer 27

the derivative would just be x right?

Answer 28

Yes

Answer 29

The derivative of y equals the slope, therefore....

3. Set y' = 1/2:

1/2 = x

Answer 30

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

and got \[y' = x\]

Answer 31

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

Answer 32

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

Answer 33

I hope that makes sense

Answer 34

ahhh i gotcha.. perfect sense

Answer 35

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

Answer 36

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!

Answer 37

:o)