A planar trajectory of a particle is modeled implicitly by (xy)+x^ 2 =3
MATHEMATICS · Multi-part · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability
Problem
A planar trajectory of a particle is modeled implicitly by
sin(xy)+x2=3.
Only points with integer coordinates are relevant in the laboratory setup.
Investigate the behavior of the particle at such points.
(a) Determine every point with integer coordinates that lies on the curve.
(b) For each point found in part (a), determine whether the point is critical. Show complete algebraic justification.
(c) State the collection of critical points with integer coordinates, giving a brief reason for discarding any extraneous solutions discovered during your work.