Word Problem

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A space traveler is moving from left to right along the curve y=x^2. When she shuts off the engines, she will continue traveling along the tangent line at the point where she is at that time. At what point should she shut off the engines in order to reach the point (4,15).

I have no idea how to do this. I was thinking of finding the tangent line, which would be y-16=8(x-4) or y=8x+12. But after that I wasn't sure of where to go or what to do.
 
Let (p, p^2) be a point on the curve where the tangent passes through (4, 15).

Equate the slope of the line passing through (p, p^2) and (4, 15) with the slope of the curve at (p, p^2), to solve for p.

I think you're ok to go from there.
 
Thank you for answering me. I'm a little confused on what the p's are? Do i just choose them or how do I solve for them? Thanks again
 
I just let the x-ordinate of the point we're looking for be p out of randomness and/or a bias I have for choosing the letter p; I don't know. The y-ordinate is p^2 from the curve's equation.
 
I'm sorry, I'm being really stupid tonight. Do I use the tangent line that I gave to you? And if so , what do I do with (x, x^2)? I thought I had to use the points (4,15)
 
The tangent you gave me doesn't pass through (4, 15).

First find p, then you have the slope of the tangent.

Then you can use either (p, p^2) -- with your values for p and p^2 -- or (4, 15) to find the tangent's equation.
 
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