Provide an appropriate response.Does the graph of f(x) =   have a tangent at the origin? Give reasons for your answer.

What will be an ideal response?


The graph does not have a tangent at the origin. The slope of the tangent lines as x approaches 0 from the left is -2, whereas the slope of the tangent lines as x approaches 0 from the right is 1. Since the one-sided limits are not equal, then, according to the limit definition of the slope of the tangent line, no tangent line exists.

Mathematics

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