Suppose that P2(x)=a+bx+cx2 is the second degree Taylor polynomial for the function f about x=0.

Question

Suppose that  is the second degree Taylor polynomial for the function  about . What can you say about the signs of a, b, c if  has the graph given below?

 

a is _

b is _

c is _

Answer 1

Since f(0)>0, a is positive.

Since the function presumably opens upward, c>0

b is responsible for shifting the graph to the left and is therefore positive.