Rate of Change

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An approximate instantaneous rate of change can be determined by estimating the slope using short intervals. 1) Graph: slope of secant OR draw a tangent, use a point on the tangent close to P and determine slope. 2) Table of values: choose a point near P and find slope. 3) Equation: use a short interval between P and Q found using an equation.

Relation between Instantaneous Rate of Change and Tangent Slope

~As a point Q becomes very close to a tangent point P, the slope of the secant line approaches the slope of the tangent line. ~As Q-->P, the slope of secant PQ--> the slope of tangent at P. ~So, the average rate of change between P and Q becomes closer to the value of the instantaneous rate of change at P.

Tangent Slope – slope of a line that touches the graph at one point, P, within a small interval.

= exact rate of change at a specific value for x; estimated using average rates of change for very small intervals.

the average rate of change over an interval is equivalent to the slope of the secant line passing through two points. Average rate of change = Δy/Δx

Relation between Average Rate of Change and The Slope of Secant

= change that takes place over an interval

Rate of Change

a measure of the change in quantity(dependent variable) with respect to a change in another quantity(independent variable).

Instantaneous Rate of Change

Average Rate of Change