Let . Determine the coefficients , , , and so that , , , and…

MATHEMATICS · Subjective · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Let p(x)=a(x−2)3+b(x−2)2+c(x−2)+dp(x)=a(x-2)^{3}+b(x-2)^{2}+c(x-2)+d. Determine the coefficients aa, bb, cc, and dd so that p(2)=4p(2)=4, p′(2)=0p'(2)=0, p′′(2)=−3p''(2)=-3, and p(3)=5p(3)=5.

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