Explain, in one or two sentences, why ensuring that a polynomial has the same value…

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

Explain, in one or two sentences, why ensuring that a polynomial

p(x)

has the same value and first derivative as a differentiable function

f(x)

x=0

guarantees that

p(x)

approximates

f(x)

to at least first order near the origin.