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# 8.7: Tangents to a Curve

Difficulty Level: At Grade Created by: CK-12
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Practice Tangents to a Curve

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### Vocabulary Language: English Spanish

secant

A line that intersects a circle in two points.

tangent

A line that intersects a circle in exactly one point.

Average rate of change

The average rate of change of a function is the change in $y$ coordinates of a function, divided by the change in $x$ coordinates.

Differential calculus

Differential calculus is the branch of calculus based on finding the difference in location between two points that get closer together until the distance between them is infinitely small.

instantaneous rate of change

The instantaneous rate of change of a curve at a given point is the slope of the line tangent to the curve at that point.

secant line

A secant line is a line that joins two points on a curve.

Slope

Slope is a measure of the steepness of a line. A line can have positive, negative, zero (horizontal), or undefined (vertical) slope. The slope of a line can be found by calculating “rise over run” or “the change in the $y$ over the change in the $x$.” The symbol for slope is $m$

Tangent line

A tangent line is a line that "just touches" a curve at a single point and no others.

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