lect116_7rev_f11

lect116_7rev_f11 - Thursday September 22 Lecture 7 :...

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Thursday September 22 Lecture 7 : Differentiation. ( Refers to Section 3.1 and 3.2 of your text ) Students who have mastered the content of this lecture know about : The definition of tangent line, average rate of change of a function over an interval, the two limit expressions which produce the slope of the tangent line to f(x) at a, the average velocity, the instantaneous velocity, the formal definition of f’(a), the formal definition of the function f’(x), the rate of change of f(x) at x = a, left-hand derivative, right-hand derivative. Students who have practiced the techniques presented in this lecture will be able to : Find the equation of a tangent line to the curve of f(x) at x=a, find the instantaneous velocity of an object for which the position function is given, find the derivative of a simple function by using the definition of the derivative. 7.1 Definitions If b > a , and f is a function on the interval [ a , b ] the quotient is called the average rate of change of the function f over the interval [ a , b ] Suppose the function f ( x ) is continuous at the point a . Let P denote the point on the curve of y = f ( x ) whose coordinates are ( a , f ( a )). We define the tangent line to the curve y = f ( x ) at P as the line through P whose slope is If this limit is equal to plus or minus infinity we will say that the curve of f ( x ) has a vertical tangent line at a . 7.1.1
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This note was uploaded on 12/28/2011 for the course MATH 116 taught by Professor Robertandre during the Spring '11 term at Waterloo.

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lect116_7rev_f11 - Thursday September 22 Lecture 7 :...

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