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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 18.01 Single Variable Calculus Fall 2006 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . Lecture 11 18.01 Fall 2006 Lecture 11: Max/Min Problems Example 1. y = ln x (same function as in last lecture) x x =e 1/e Figure 1: Graph of y = ln x . x 1 What is the maximum value? Answer: y = . e Where (or at what point) is the maximum achieved? Answer: x = e . (See Fig. 1).) Beware: Some people will ask What is the maximum?. The answer is not e . You will get so used to finding the critical point x = e , the main calculus step, that you will forget to find the maximum 1 1 value y = . Both the critical point x = e and critical value y = are important. Together, they e e 1 form the point of the graph ( e, ) where it turns around. e Example 2. Find the max and the min of the function in Fig. 2 Answer: If youve already graphed the function, its obvious where the maximum and minimum values are.are....
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lec11 - MIT OpenCourseWare http://ocw.mit.edu 18.01 Single...

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