MATH 121 – Test #3 Study Guide
Section 3.2
 know and apply Rolle’s Theorem, finding c ε (a, b) such that the tangent at c is horizontal
 know and apply the Mean Value Theorem, finding c ε (a, b) such that the instantaneous rate
of change at c equals the average rate of change from a to b
Section 3.3
 know and use the Increasing/Decreasing Test, based on f ´(x)
 know definitions of first-order and second-order critical points
 know and use the First Derivative Test to determine if there exists a local min or max at a
first-order critical point
 know definitions of concavity and inflection point
 explain how concavity relates to the change in a graph’s slope and, equivalently, the
change in a function’s first derivative.
 know and use the Concavity Test, based on f ´´(x)
 know and use the Second Derivative Test to determine if there exists a local min or max at
a first-order critical point
Section 3.4
 use all the tools from Section 3.3 (and also knowledge of asymptotes) to sketch curves
Section 3.5
 set up and solve optimization problems similar to p. 176 - #2-13, 19-22, 37
Section 3.6
 know and apply Newton’s Method to approximate the root of a function
 explain how this method relates to a function’s linearization at a point x
 describe three or four situations where Newton’s Method is likely (or guaranteed) to fail
Section 3.7
 compute the general antiderivative of: polynomials, power functions, and derivatives of the
six trig functions
 solve problems similar to p. 189- #13-28, 33-36, 44, 45
Section 4.1
 approximate the area under a curve from a to b using rectangles based on right-hand and
left-hand endpoints
 for a given function explain whether (and why) these two methods yield underapproximations or over-approximations