Question

Sketch the parabolas y = x^2 and y= (x^2) - 2x + 2. Is there a line that is tangent to both curves? If so, find the equation. If not, why not?

Can someone please help me with this? Due tomorrow morning ;(

Answer 1

Well I'm not sure but to me if you can get a line that passes through the center of both parabolas then there is.

Answer 2

The only reasons there wouldn't be one if there was a shift in the parabola

Answer 3

in respect to the other parabola but I forgot how to check the shift.

Answer 4

what class is this for ?

Answer 5

In Calc, we're learning about derivatives now. So I'm guessing there has to be derivatives involved.

Answer 6

Calculus.

Answer 7

oh if the derivative of both lines are the same

Answer 8

parabolas

Answer 9

you know how to find derivatives right?

Answer 10

Did you do calculus already?

Answer 11

Yeah, I found the derivatives of both functions. 2x and 2x-2

Answer 12

to HairtUB: I looked at your picture. The slope between both functions is 1.

Answer 13

so I guess no is the answer since both are not the same. Can anyone else confirm this?

Answer 14

yea i can confirm your answer becasuse they never have the same slope at the same point

Answer 15

I found a solution to this problem online. However, it's not finished and I cannot follow the logic at all.

Answer 16

post the solution you found

Answer 17

http://math.berkeley.edu/~preskill/math1a/worksheet3soln.pdf

Answer 18

it look to me like you cant find a solution of x that satisfys both equations thats why its left blank

Answer 19

@jdad56: Hm, I was thinking the same thing. But for some reason, judging by the graphs, it seems that visually there were a tangent to both curves at the vertex.

Answer 20

I have y=x-0.25. But I only got it through trial and error :/

Answer 21

Ah, this problem is so difficult. I'm thinking if setting both derivatives equal to one another and solving, the problem does not solve. Therefore, that might imply that there is no tangent line to both curves? Is my reasoning correct for this?

Answer 22

That's what I thought as well, but the x values aren't the same for both derivatives.

Answer 23

Yeah, because of the shift.

Answer 24

Something happened earlier. What were you saying?

Answer 25

You can see from the graph that they overlap but the tangents can never be the same the lowest value for y in the x^2-2x-2 is (1,1) and this is the point of intersection but the tangents are different here

Answer 26

actually here is a better graph. you could take the derivative to prove it...

Answer 27

so thats 2x and 2x-2
so thegradients are 2 and 0 respectively

Answer 28

Thank you, @kevsturge. I really appreciate it!