Determine whether or not x=0 is a point of relative extremum of the .pdf

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Determine whether or not x=0 is a point of relative extremum of the following function: a) g(x)= sinx-x b) k(x)=cosx -1 + 1/2x2 Solution a) g(x)= sinx-x g\'(x) = cosx-1 g\'(x) = 0 at cosx = 1 means x=0 g\'\'(x) = -sinx g\'\'(x) = 0 so it is a point of inflection b) k(x)=cosx -1 + 1/2x2 k(x) = cosx-1+1/2x^2 k\'(x) = -sinx+x at x = 0 it is zero k\'\'(x) = -cosx+1 k\"(x) = 0 at zero it is also a inflection point.

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