# lec10 - MIT OpenCourseWare http/ocw.mit.edu 18.01 Single...

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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 .

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Lecture 10 18.01 Fall 2006 Lecture 10: Curve Sketching Goal : To draw the graph of f using the behavior of f and f . We want the graph to be qualitatively correct, but not necessarily to scale. Typical Picture: Here, y 0 is the minimum value, and x 0 is the point where that minimum occurs. x 0 = critical point y 0 Figure 1: The critical point of a function Notice that for x < x 0 , f ( x ) < 0. In other words, f is decreasing to the left of the critical point. For x > x 0 , f ( x ) > 0: f is increasing to the right of the critical point. Another typical picture: Here, y 0 is the critical (maximum) value, and x 0 is the critical point. f is decreasing on the right side of the critical point, and increasing to the left of x 0 . x 0 = critical point y 0 f’(x) < 0 x > x 0 Figure 2: A concave-down graph 1
Lecture 10 18.01 Fall 2006 Rubric for curve-sketching 1. (Precalc skill) Plot the discontinuities of f especially the in±nite ones! 2. Find the critical points. These are the points at which f ( x ) = 0 (usually where the slope changes from positive to negative, or vice versa.) 3. (a) Plot the critical points (and critical values), but only if it’s relatively easy to do so.

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## This note was uploaded on 01/18/2012 for the course MATH 18.01 taught by Professor Brubaker during the Fall '08 term at MIT.

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lec10 - MIT OpenCourseWare http/ocw.mit.edu 18.01 Single...

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