Fall 2025 Final Exam Review
Here is the final exam review. I will post the video lectures on this post as well from the next two classes.
Fall 2025 Chapter 3-9
Topics Covered:
Solving a geometric related rates problem
Solving a trigonometric related rates problem
Fall 2025 Chapter 3-7 and 3-8
Topics Covered:
Using differentiation to analyze the motion of a particle
Evaluating an exponential function with base e that models a real-world situation
Finding a final amount in a word problem on exponential growth or decay
Finding a particular solution to an initial-value problem involving growth and decay
Writing and solving an initial value problem modeling growth or decay
Fall 2025 Chapter 3-6
Topics Covered
Finding the derivative of a combination of logarithmic and algebraic functions
Finding the derivative of a composition involving logarithmic and trigonometric functions
Finding a derivative using logarithmic differentiation
Finding the derivative of the six basic inverse trigonometric functions
Finding the derivative of a composition involving an inverse trigonometric function and an algebraic function
Fall 2025 Chapter 3-4 and 3-5
Topics Covered:
Finding the derivative of a composition of algebraic functions
Using a combination of the Chain, Product, and Quotient Rules to find a derivative
Introduction to implicit differentiation
Finding a derivative using implicit differentiation
Fall 2025 Chapter 3-3
Topics Covered:
Finding the derivatives of the six basic trigonometric functions
Finding the derivative of a function involving sine or cosine
Finding higher order derivatives of functions involving sine and cosine
Finding the derivative of a composition of algebraic functions
Finding the derivative of a composition of functions: Exponential
Using a combination of the Chain, Product, and Quotient Rules to find a derivative
Fall 2025 Chapter 3-1 and 3-2 Notes
Topics Covered:
Finding the derivative of a power function
Finding the derivative of a linear combination of power functions
Finding the derivative of a linear combination of power functions and ex
Finding higher order derivatives of a linear combination of power functions
Finding an equation of the tangent line or normal line to a curve at a point
Finding the x-coordinates of points on a curve where the tangent line is horizontal
Finding the derivative of a product involving sums of power functions
Finding the derivative of a product involving power functions and ex
Finding the derivative of a quotient involving sums of power functions
Finding the derivative of a quotient involving power functions and ex
Applying rules of differentiation given information about two functions
Applying the Product and Quotient Rules of differentiation given the graphs of two functions
Fall 2025 Chapter 2-7 and 2-8 Notes
Topics Covered
Finding a derivative at a given number by simplifying a difference quotient
Relating information about a function and its derivative to the equation of a tangent line
Interpreting the graph of a function to order the values of its derivative at several values
Understanding instantaneous and average rates of change
Finding a derivative by simplifying a difference quotient
Graphing the derivative of a piecewise linear function
Matching the graph of a function with the graph of its derivative
Finding a derivative by simplifying a difference quotient
Interpreting the graph of a function to analyze whether or not it is differentiable at various x-values
Analyzing points on the graph of a function for differentiability
Fall 2025 Chapter 2-6 Notes
Topics Covered
Limits at infinity and graphs
Limits at infinity and rational functions
Limits at infinity and functions involving a sum or quotient with a radical
Evaluating limits to find the vertical and horizontal asymptotes of a function