`x=3t^2 , y=t^3-t` Determine the open t-intervals on which the curve is concave downward or concave upward.

Expert Answers

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Given parametric equations are:


We need to find the second derivative, to determine the concavity of the curve.


Let's take the derivative of x and y with respect to t,














Curve is concave upwards if second derivative is positive and concave downwards if it is negative,

So, the curve is concave upward for `t>0`

Curve is concave downward for `t<0`

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