The parametric curve is given for by x(t)=2t- t

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

The parametric curve CC is given for 0≤t≤2π0\le t\le 2\pi by x(t)=2t−sin⁡t,y(t)=3−cos⁡t.x(t)=2t-\sin t, \qquad y(t)=3-\cos t. For which value(s) of tt does CC have a point of inflection? (a) t=π2  and  t=3π2t=\dfrac{\pi}{2}\;\text{and}\;t=\dfrac{3\pi}{2} (b) t=π3t=\dfrac{\pi}{3}\; only (c) t=π3  and  t=5π3t=\dfrac{\pi}{3}\;\text{and}\;t=\dfrac{5\pi}{3} (d) t=2π3  and  t=4π3t=\dfrac{2\pi}{3}\;\text{and}\;t=\dfrac{4\pi}{3}

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