LIFESCI 30A Lecture Notes - Lecture 11: Trigonometric Functions
28 Oct 2016
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Let f be a function of time (t) (on monday this was x(t), we"re switching notation to f(t)) Average rate of change over time interval [t1, t2] Average rate of change = f(t2)-f(t1)/(t2-t1) = df/dt = change in f/change in time. = slope of the secant line that cuts through the graph of f at points (t1, f(t1) and (t2, f(t2)) Instead of t1 and t2, use a and x. This is the graph of the secant line. (a, f(a)) are coordinates on the graph. L is the secant line that passes through this point and another point on the graph f"(t) = the derivative of the function f at t1 = the limit as dt 0 of df/dt. = the limit as t2 t1 of f(t2) f(t1)/t2-t1. This is known as the instantaneous rate of change of f at t1 (slope of the tangent line to the graph of f)
