Honors Mathematics 3 Practice Exam

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For the parametric curve x = t^2, y = t, what is dy/dx when t = 3?

1/4

1/5

1/7

1/6

To find the slope of a parametric curve, use dy/dx = (dy/dt)/(dx/dt). Here y = t gives dy/dt = 1, and x = t^2 gives dx/dt = 2t. So dy/dx = 1/(2t). At t = 3, that becomes 1/(2·3) = 1/6. Since dx/dt ≠ 0 at t = 3, the slope is well-defined.

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