Verifying Tangent Lines

00:00 2 marks

Consider a graph of a continuous function and a straight line that appears to be tangent to the curve at a single point. Explain how calculus, specifically the concept of the derivative, can be used to rigorously verify if this line is indeed a tangent. Clearly state the fundamental condition for tangency in terms of derivatives and slopes.

Hint Hint

Hint

The derivative of a function at a point gives the slope of the tangent line at that point. Use this relationship to define the condition for tangency.

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Answer Answer

Complete Answer

A line is tangent to a curve at a given point if and only if the slope of the line is equal to the derivative of the function at that point.

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