Assigned work: pg.83 #2, 4def, 5, 11e, 21-24 Differential Calculus – rates of change Integral Calculus – area under curves Rates of Change: How fast is.

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Assigned work: pg.83 #2, 4def, 5, 11e, Differential Calculus – rates of change Integral Calculus – area under curves Rates of Change: How fast is the ‘y’ changing with respect to ‘x’ changing Slope of a line is a constant rate of change. S. Evans

1.2 Slope of a Tangent Tangent Line: A line that touches the curve at a single point in a small region. Its slope represents the rate of change of the curve at that point. Let’s derive a formula for the slope of a tangent line at a specific x value called ‘a’………….. S. Evans

1.2 Slope of a Tangent Deriving the Slope of a Tangent Line: Note the curve below does not have a constant rate of change but we can find the rate of change at x = a. y Slope of Secant PQ Q P As PQ becomes the slope of the tangent at ‘a’ a a+h x Slope of Tangent S. Evans

1.2 Slope of a Tangent Ex 1: Find the slope of the tangent at the point (3,10) to the curve Solution: Watch your Form! leave limit sign until after you cancel the ‘h’ and sub in value S. Evans

1.2 Slope of a Tangent Ex 2: a) Find the slope of the tangent to the curve at x=4. S. Evans

1.2 Slope of a Tangent Ex 2: b) Find equation of the tangent to the curve at x=4. (slope found in a) now we just need a point) so point is (4,2) Equation of Tangent in Point slope Form: S. Evans