AP Calculus Homework: Finding Intervals of Increase and Points of Inflection

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In summary, we discussed a function f defined on the closed interval -3<= x <= 4 with f(0)=3, whose derivative consists of one line segment and a semicircle. We also considered the intervals on which f is increasing and the x-coordinates of the points of inflection on the open interval -3<x<4. In addition, we looked at the function f defined by a power series and used the LaGrange error to approximate f(1) with an error less than 1/100. We also questioned whether f(-3) and f(4) could be found by calculating the area under the graph of f '.
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nns91
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Homework Statement



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.


Homework Equations



LaGrange error

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 ?
 
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  • #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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