is this statement true? If f'(x)=0 for all in an interval (a, b), then f(x)=0 for all x in the interval (a, b).
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Originally Posted by Baatata is this statement true? If f'(x)=0 for all in an interval (a, b), then f(x)=0 for all x in the interval (a, b). what would be the value of f'(x) in (a,b) if f(x) = 1 ?
Originally Posted by Baatata is this statement true? If f'(x)=0 for all in an interval (a, b), then f(x)=0 for all x in the interval (a, b). No, f could be another constant.
If f(x)=0 implies that f'(x)=0 . However, the same can be said for any constant c. Thus, f(x) = c implies that f'(x)=0.
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