Consider the following cubic polynomial f(x)f(x) and related polynomials: f′(x),f′′(x),f′′′(x) f(x)=ax3+bx2+cx+d f′(x)=3ax2+2bx+c f′′(x)=6ax+2b f′′′(x)=6a Determine values of the coefficients a,b,c,d so that these polynomials simultaneously satisfy the conditions f(1)=1, f′(1)=1, f′(1)=−7, f′′(1)=−10,  f′′′(1)=−12

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