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I was understanding derivative function when I thought that why "concept of tangent", was invented.If it was so because of influence of Physics - instantaneous velocity and other stuff then why tangent line is best fit to get the rate of change of y versus x ,and most importantly "how it would be defined in this sense"**I am following **Michael Spivak's book he has defined it slope as limit of slope of secant lines but would that limit always equal slope of tangent line when we define it in this way.please help!!

Hitesh Pathak
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  • Does http://math.stackexchange.com/a/19636/259262 help? – Patrick Stevens Sep 11 '15 at 14:09
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    No, it will NOT "always give the slope of the tangent line" because some functions are NOT differentiable at every point. In fact, the definition of "differentiable at a point" is that this limit exists. It is true that if the limit exists then it must be equal to the slope of the tangent line. – user247327 Sep 11 '15 at 14:14

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