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Is “the slope of the tangent to a curve at a point” the same as “the slope of the curve at a point”? Can a single point have a slope or is it only defined for two or more points that form a straight line?

Furthermore is the “slope” of a function the same as the “rate of change” of a function? Because I never see people saying the “slope” of a function but only the “rate of change” of a function which has lead me to believe that “slope” is purely a geometric concept. Correct me if I am wrong. Thanks in advance.

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Yes it is, the slope or gradient of the curve is the same as the slope or gradient of the tangent at that same point, but a single point can not have a slope. Because the slope is the ratio of the difference in y- coordinates and x- coordinates. Secondly, the slope of a function is not the rate of change but rather the gradient function is the same as the rate of change.

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