AMS 11A Chapter Notes - Chapter 11.1: Difference Quotient
18 Oct 2016
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If the difference z - a is called h, then we can write z as a + h (where h 0) If the coordinates of p are (a, f(a)), and the coordinates of q are (z, f(z)), then the slope of the secant line pq is: So, the limiting value of the slopes of the secant lines (the slope of the tangent line at (a, f(a)) is: Find the slope of the tangent line to the curve = (cid:4666) (cid:4667)= 2at the point (1, 1) Therefore, the tangent line to = 2at point (1, 1) has a slope of 2. The slope is the limit with f(x) = x^2 and a = 1. 1+2 + 2 1 derivative - the slope of a line tangent to a curve. Example: (1, 7) is called a difference quotient. The derivative of a function f is the function denoted f" (read f prime ) and defined by:
lies on the curve 
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, use your calculator to find the slope of the secant line PQ ( correct to six decimal places) for the following values.
