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Math 2.0

Real functions Concept

Tangent line

Builds on Derivative

Summary

Let $f$ be differentiable at $a$ . The tangent line to the graph of $f$ at $(a, f(a))$ is the line $y = f(a) + f'(a)(x - a)$ . It is the line through this point that best fits the graph near it.

Remarks

The tangent line is the limit of the secant lines through $(a, f(a))$ and $(x, f(x))$ as $x \to a$ . The error $f(x) - f(a) - f'(a)(x - a)$ is $o(x - a)$ as $x \to a$ . This property characterizes the derivative. For $f(x) = x^2$ at $a = 1$ , the tangent line is $y = 2x - 1$ .

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Limit point of a set definition
Limit of a function definition
Derivative definition
Tangent line concept

Further reading

Web https://en.wikipedia.org/wiki/Tangent, Tangent line to a plane curve

About this page

Tag	`01R1HW3Y42`
URI	`m2://01R1HW3Y42`
Kind	concept
Writing	W1 stated
MSC	26A24
Uses	Derivative
Same as	Wikidata Q131251 Wikipedia Tangent

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