Measuring the Rate of Change at a Point on a Curve (AQA A-Level Biology): Flashcards

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Measuring the Rate of Change at a Point on a Curve
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Definition of a tangent line on a curve

Line that touches curve at exactly one point

What a tangent represents at a point on a curve

Instantaneous rate of change at that point

Formula for gradient of a tangent line

change in ychange in x\frac{\text{change in y}}{\text{change in x}}

How tangent should touch curve at point of interest

Should touch only, not cross the curve

Shape used to measure gradient from tangent line

Right-angled triangle with hypotenuse on tangent

What gradient of tangent equals

Rate of change at that point on curve

Meaning of negative gradient on a curve

Indicates decreasing values

Meaning of positive gradient on a curve

Indicates increasing values

What must be included in rate of change answer

Appropriate units

Why tangent line method works for rate measurement

Tangent has same gradient as curve at contact point

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