1. ## Another Newton

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.

2. Originally Posted by sheva2291
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

3. Do you mean $y= e^{cos x}$?

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.