Consider the parametric curve
x = t2, y = t3 + 3t, −∞ < t < ∞.
(a) Find all of the points where the tangent line is vertical.
(b) Find d^{2}y/dx^{2} at the point (1, 4).
(c) Set up an integral for the area under the curve from t = −2 to t = −1.
(d) Set up an integral for the length of the curve from t=−1 to t=1.
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