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