MATH 140 Lecture Notes - Lecture 23: Inflection, Second Derivative
9 Nov 2015
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The graph of f is concave upward on an interval i if f " is increasing on i . The graph of f is concave downward on an interval i if f " is decreasing on i . Note: concavity is always on an open interval. Suppose that the graph of f has a tangent line (which may be vertical) at the point ( c , f ( c )) and f "" changes sign at ( c , f ( c )); then ( c , f ( c )) is an inflection point of the graph of f . 1 3 f (x) x and if x. = 3 2 x 2 x if x o f. = 6 1 x: find relative extrema, concavity, inflection points, y-intercept, and graph, extrema: (x) = 3 2 x 2 = 0 f ( ) f( ) = 2 when x infl. pt. at ( , f( ))
