1.
Consider the function f(x)=x3sinxcosx610pp2p3f(x) = \begin{vmatrix} x^3 & \sin x & \cos x \\ 6 & -1 & 0 \\ p & p^2 & p^3 \end{vmatrix} where pp is a constant. What is the value of pp for which f(0)=0f''(0) = 0?