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Which answers is admissible for this problem?
A spaceship moves along y = x^3 - 8x in the positive x-direction. Shutting off the engines at P allows it to move off along the tangent at P. Find P so that the ship can reach the point (4, 0).
I solved this problem and got:
x = 2
x = -1.46
x = 5.46
Which one of these x values would be admissible for this problem?
1 Answer
- MathMan TGLv 71 decade agoFavorite Answer
It's as simple as saying "Is x < 4 ?"
(once you have the solutions to the other equation,
(x^3 - 8x) / (x - 4) = 3x^2 - 8, which is another cubic).
Look at the conditions:
"A spaceship moves along y = x^3 - 8x in the positive x-direction"
Since x is moving in the positive direction,
the 5.46 value is already past 4,0.
The spaceship would have to reverse course to reach 4,0.
In this picture, http://i34.tinypic.com/2ppwivc.jpg
that is the green line and it would have to be coming down and to the left, but it is moving up and to the right on the curve.
For the other two points (red and blue lines) it works out ok,
since the ship is to the left of the point 4,0 and moving
to the right.
