Question

Determine the points of inflection of the function.
f(x) = x + sin x (−2π ≤ x ≤ 2π)

Answer 1

Points of inflection are points on the curve where the curvature changes sign.
Since the sign of curvature is equal to the sign of the second derivative, so the points of inflection can be found to be where the second derivative changes sign.

For
f(x)=x+sin(x),
f'(x)=1+cos(x)
f"(x)=-sin(x)
Make a plot of -sin(x) and you should find that f"(x) changes sign at x=0,π and 2π.

The inflection points are therefore at __, __, and __ according to the definition.

Answer 2

y=100 find the first and second derivative