Find the cubic polynomial that satisfies , ,

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Find the cubic polynomial p(x)=ax3+bx2+cx+dp(x)=ax^{3}+bx^{2}+cx+d that satisfies p(0)=0p(0)=0, p′(0)=1p'(0)=1, p′′(0)=−1p''(0)=-1, and p′′′(0)=2p'''(0)=2. Write p(x)p(x) in standard form.

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