The motion of a particle traces the curve ,

MATHEMATICS · Multi-part · A Level · Mathematics · Differentiation · Differentiation

Problem

The motion of a particle traces the curve x=2t+1x = 2t + 1, y=t2−4t+3y = t^{2} - 4t + 3, for all real tt. (i) Calculate d2ydx2\dfrac{d^{2}y}{dx^{2}} as a function of tt. (ii) Show that the concavity of the curve is the same at every point and specify whether the curve is concave upward or concave downward. (iii) Find the coordinates of the point corresponding to t=3t = 3 and write the equation of the tangent line at that point.

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