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Some other AP problems

  1. Apr 2, 2009 #1
    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 ?
     
  2. jcsd
  3. Apr 2, 2009 #2
    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 ' ?
     
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