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How do you determine the slope of a tangent line? Why does this work?

Answer 1

Find #frac{dy}{dx}#.

A tangent line is usually tangent to a curve at a point #P#. You would have to find #frac{dy}{dx}# of the curve at #P#, and that is the same as the slope of the tangent line.

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Answer 2

Scarlett Allison

To determine the slope of a tangent line, you can use the derivative of the function at the point of tangency. The derivative represents the rate of change of the function at any given point. By evaluating the derivative at the point of tangency, you can find the slope of the tangent line. This works because the derivative measures the instantaneous rate of change of the function, which is precisely what the slope of the tangent line represents.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.