Some other AP problems

1. Apr 2, 2009

nns91

1. The problem statement, all variables and given/known data

1. Let f be a function defined on the closed interval -3<= x <= 4 with f(0)=3. The graph of f's, the derivative of f, consists of one line segment and a semicircle.
(a). On what intervals is f increasing ?
(b). Find the x-coordinate of each point of inflection of the graph of f on the open interval -3<x<4.

2. The function f is defined by the power series

f(x)=$$\sum$$ (-1)^n*x^2n / (2n+1)! for all real numbers x

a. Show that 1-1/3! approximates f(1) with error less than 1/100.

2. Relevant equations

LaGrange error

3. The attempt at a solution

1.
a. Is that true to say f is increasing when f is positive ?
b. Is that true to say the inflection point occurs when slope of f ' = 0 ? Or it also has to satisfy the change in sign of curvature ?

2. Do I use LaGrange for this to approximate the error or how should I do it ?

2. Apr 2, 2009

nns91

1. Also for number one. I need also to find f(-3) and f(4). Do I just calculate the area under the graph of f ' ?