For the following problem, we are asked to find dy/dx, [d^2 * y] / [d * x^2], and to state for which values of t is the curve concave upward.
1. x = t^3 -12t, y = t^2 – 1
(the first equation reads as x equals t cubed minus 12t; the second equation reads as y equals t squared minus 1).
For this problem I got:
2t / [3t^2 – 12] for dy/dx;
[-6t^2 – 24] / [(3t^2 – 12)^3] for [d^2 * y] / [d * x^2];
after setting [d^2 * y] / [d * x^2] equal to 0 I had:
6t^2 + 24 = 0, and thus t^2 = -4;
Assuming I did all of this right so far, does this mean that the function does not concave upward anywhere because the square root of negative 4 is a non-real answer, or does is still concave up somewhere? Please explain which is the case and why, and if I did something wrong earlier in the problem (i.e. an algebraic error somewhere), please explain how to do the problem step-by-step.
2007-10-17
10:29:53
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1 answers
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asked by
Ryan_1770
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