Another Newton

May 2010
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Use Newton's method to find the coordinates of the inflection point of the curve y = ecos(x),
0 ≤ x ≤ π , correct to six decimal places.
 

CaptainBlack

MHF Hall of Fame
Nov 2005
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Use Newton's method to find the coordinates of the inflection point of the curve y = ecos(x),
0 ≤ x ≤ π , correct to six decimal places.
Your notation is not clear, but an inflection point is a point at which the curvature changes sign, in practice this means that it is a local extrema of y'.

CB
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
Do you mean \(\displaystyle y= e^{cos x}\)?

As Captain Black said, an inflection point occurs at a local extremum of y' which, in turn, mean that y"= 0 (since y" always exists for this function).

Take the second derivative of this function, set it equal to 0 and use Newton's method to solve the equation.
 
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