A quadratic polynomial is intended to approximate near

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

A quadratic polynomial

P(x)=1+x+cx^{2}

is intended to approximate

f(x)=\ln(1+x)

near

x=0

. Determine the value of

c

that ensures

P

and

f

have identical first and second derivatives at

x=0

. (a)

-\dfrac12

(b)

-1

(c)

\dfrac12

(d)

-2