M119 Study Guide Test 2: Chapters 2 and 3 Understand that the derivative at a point, f ′ (a) gives the instantaneous rate of change of the function at the point x = a, while the slope of a line that connects two points gives the average rate of change. Be able to estimate the derivative of a function at a point, given the function in the form of a graph, table of values, or a formula. Be able to use both notations for the derivative and the second derivative. Be able to interpret the practical meaning of statements involving the derivative. Use appropriate units for the derivative in application problems. Be able to estimate the value of a function at a point using local linear approximation. Know the difference between f (a), f ′ (a), and f ″ (a). Be able to determine the sign of each when given a graph of the function. Be able to compare values of f, f ′ or f ″ at different points. Understand the relationship between the sign of f ′ and whether f is increasing or
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