Let . Which statement about is…

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

Problem

Let r(t)=⟨t2,∣t∣⟩\mathbf{r}(t)=\langle t^{2},|t|\rangle. Which statement about r′(0)\mathbf{r}'(0) is true? (a) r′(0)=⟨0,0⟩\mathbf{r}'(0)=\langle 0,0\rangle because both one–sided limits equal zero. (b) r′(0)\mathbf{r}'(0) does not exist because the second component is not differentiable at t=0t=0. (c) r′(0)=⟨0,1⟩\mathbf{r}'(0)=\langle 0,1\rangle since the right–hand derivative of ∣t∣|t| is 11. (d) r′(0)\mathbf{r}'(0) does not exist because the first component has a cusp at t=0t=0.

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