2.1A Tangent Lines & Derivatives

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Presentation transcript:

2.1A Tangent Lines & Derivatives

Tangent Line: a line that intersects a curve at a point P & whose slope approximates the behavior of the curve at or very close to point P. Slope = Instantaneous Rate of Change at P

Secant Line: a line that intersects a curve at two points, P & Q Secant Line: a line that intersects a curve at two points, P & Q. Slope = Average Rate of Change between P & Q

P = (a, f(a)) with a slope of, Tangent Line to f (x) The line through P = (a, f(a)) with a slope of,

Ex 1: Find the slope of the tangent line at x = 3

Derivatives The derivative of f is:

Ex 2: Find f (x) and use it to find the equation of the tangent line to f (x) at x = 1.

2.1A pg. 103 # 1, 3, 4, # 9 – 33 EOO, # 71, & 77 (use slope limit for 9,71 & 77)

Ex 3: Find the slopes of the tangent lines to the graph at (0, 1) and (−1, 2).