2.4 Rates of Change and Tangent Lines Calculus. Finding average rate of change.

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Presentation transcript:

2.4 Rates of Change and Tangent Lines Calculus

Finding average rate of change

Slope of a secant line Use points P(23, 150) and Q(45, 340) to compute the average rate of change and the slope of the secant line PQ. Use points P(23, 150) and Q(45, 340) to compute the average rate of change and the slope of the secant line PQ. 8.6 flies/day 8.6 flies/day We can always think about average rate of change as the slope of a secant line. We can always think about average rate of change as the slope of a secant line.

Instantaneous rate of change

Steps for finding the slope of the tangent 1.Start with what we can calculate- the slope of the secant through a point P and a point nearby (Q) on the curve. 2.Find the limiting value of the secant slope (if it exists) as Q approaches P along the curve. 3.Define the slope of the curve at P to be this number and define the tangent to the curve at P to be the line through P with this slope.

Definition: Slope of a curve at a point

Example: Finding slope and tangent line

Lines normal to a curve

Free fall…again

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