Suppose g is a function which has continuous derivatives, and that g(7)=4,g′(7)=−1, g″(7)=1, g‴(7)=1. (a) what is the taylor polynomial of degree 2 for g near 7? p2(x)=

A Taylor series is a series expansion of a function about a point. A one-dimensional Taylor series is an expansion of a real function f(x) about a point x=a is given by

.

In your case a=7 and g(7)=4, g′(7)=−1, g″(7)=1, g‴(7)=1.

The Taylor polynomial of degree 2 for g near 7 is:





.

answer: yes, since the line has a steeper rate of change than the exponential the y-values will be greater and they will only intersect one time.