Consider the polynomial

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Consider the polynomial P(x)=1+bx+ax2P(x)=1+bx+ax^{2}. Find the ordered pair (a,b)(a,b) so that PP shares the same value, first derivative, and second derivative at x=0x=0 with the function F(x)=cos⁡xF(x)=\cos x. (a) (12,0)\left(\dfrac12,0\right) (b) (−12,1)\left(-\dfrac12,1\right) (c) (−12,0)\left(-\dfrac12,0\right) (d) (0,−12)\left(0,-\dfrac12\right)

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