1. The problem statement, all variables and given/known data
Find a parametric form for the part-cubic curve with equation y = x3, 0 ≤ y ≤ 8; starting point (2, 8),
3. The attempt at a solution
The question beforehand was the exact same but the starting and ending points reversed. My answer for that was; r(t) = (t, t^3) for t an element of [0,2], ill call this equation A.
So for this question is set up a few linear equations and solved them and came up with the parametric vector function; r(t) = (2-t, 8-t^3), ill call this equation B. B satisfies the starting and ending point conditions but, to me, it looks like A and B are describing different curves. When i graph them, they look different. And im not sure how to interpret it. Is it that my answer is wrong? or is it that when you reverse the order of the start and end points as you do in B, its almost as if you you are looking at the graph upside down and considering (2,8) as the origin (if that makes any sense at all). Thank you for your time.
Find a parametric form for the part-cubic curve with equation y = x3, 0 ≤ y ≤ 8; starting point (2, 8),
3. The attempt at a solution
The question beforehand was the exact same but the starting and ending points reversed. My answer for that was; r(t) = (t, t^3) for t an element of [0,2], ill call this equation A.
So for this question is set up a few linear equations and solved them and came up with the parametric vector function; r(t) = (2-t, 8-t^3), ill call this equation B. B satisfies the starting and ending point conditions but, to me, it looks like A and B are describing different curves. When i graph them, they look different. And im not sure how to interpret it. Is it that my answer is wrong? or is it that when you reverse the order of the start and end points as you do in B, its almost as if you you are looking at the graph upside down and considering (2,8) as the origin (if that makes any sense at all). Thank you for your time.
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