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CalculusChallengeThe Derivative

The Derivative · Challenge problem

Find constants a,b,ca,b,c so that

f(x)={ax2+bx+c,x<0,cos⁡x,x≥0,f(x)=\begin{cases} ax^{2}+bx+c, & x<0,\\[2pt] \cos x, & x\ge 0,\end{cases}

is twice differentiable at x=0x=0.