Let , where is a constant. Then…

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

Problem

Let f(x)=∣x3sin⁡xcos⁡x6−10pp2p3∣f(x)=\begin{vmatrix}x^3&\sin x&\cos x\\6&-1&0\\p&p^2&p^3\end{vmatrix}, where pp is a constant. Then d3dx3f(x)∣x=0\left.\frac{d^3}{dx^3}f(x)\right|_{x=0} is (1) pp (2) p+p2p+p^2 (3) p+p3p+p^3 (4) Independent of pp

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