MATH 121 Lecture Notes - Lecture 8: Diminishing Returns
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--1st derivative (gives us slope tangent line as well as intervals for increasing. and. Math 121 section 5. 3 higher derivatives, concavity: higher derivatives and their notations: f decreasing. ) f f. Business: 1st derivative marginal 2nd derivative=0 point of diminishing returns. Points of inflections will be points in the domain where the graph changes concavity. Find the open intervals where the function is concave upward or concave downward. Find the approximate coordinates of all points of inflection of the function (if any). (if there are no inflection points enter dne. ) Example 4: the graph of the derivative, f "(x), is given. Determine the x-coordinates of all points of inflection of f(x), if any. (assume that f(x) is defined and continuous everywhere in [ 9, 9]. ) pg. Example 5: the graph of the derivative, f "(x), is given. Determine the x-coordinates of all points of inflection of f(x), if any. (assume that f(x) is defined and continuous everywhere in [ 6, 6]. )
