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)=[tex]\sum[/tex] (-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 ?