Let , where and . What is…

MATHEMATICS · Single correct · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

Let p(t)=q(k(t))p(t)=q\big(k(t)\big), where q(v)=⟨v, v2, 1v⟩q(v)=\left\langle\sqrt v,\,v^{2},\,\dfrac{1}{v}\right\rangle and k(t)=sin⁡(2t2)k(t)=\sin(2t^{2}). What is p′ ⁣(π4)p'\!\left(\sqrt{\dfrac{\pi}{4}}\right)? (a) ⟨π,  4π,  −2π⟩\left\langle\sqrt{\pi},\;4\sqrt{\pi},\;-2\sqrt{\pi}\right\rangle (b) ⟨0, 0, 0⟩\langle 0,\,0,\,0\rangle (c) ⟨12,  2,  −1⟩\left\langle\dfrac12,\;2,\;-1\right\rangle (d) ⟨0,  0,  −2π⟩\left\langle0,\;0,\;-\dfrac{2}{\sqrt{\pi}}\right\rangle

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