Sketch the graph of a function defined everywhere satisfying f'(x) = 0 for every x, except at x = 0 where the derivative does not exist.

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Sketch the graph of a function defined everywhere satisfying f'(x) = 0 for every x, except at x = 0 where the derivative does not exist.

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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derivatives do not exist at cusp and corners. Are you missing any other information? f '(x)=0 means the derivative of f is zero
No, that's it. Any graph that will satisfy this will do. I assume that a graph that is horizontal the whole way (thereby having no slope) would satisfy this...I think I could make it y=1 for x's less than zero and y=-1 for x's greater than zero to satisfy the question. Sound plausible?
yes because in order for the limit to exist the right hand and left hand limits must be the same. When you take the derivative of each function, it is zero. Yes, I think this will work

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