Unit 4 Learning Outcomes

Upon successful completion of this unit, you will be able to:

• state whether a given point on a graph is a global/local maximum/minimum;
• find critical points and extreme values (max/min) of functions by using derivatives;
• determine the values of a function guaranteed to exist by Rolle's Theorem and by the Mean Value Theorem;
• use the graph of \( f(x) \) to sketch the shape of the graph of \( f(x) \);
• use the values of \( f'(x) \) to sketch the graph of \( f(x) \) and state whether \( f(x) \) is increasing or decreasing at a point;
• use the values of \( f''(x) \) to determine the concavity of the graph of \( f(x) \);
• use the graph of \( f(x) \) to determine if \( f''(x) \) is positive, negative, or zero;
• solve maximum and minimum problems by using derivatives;
• restate in words the meanings of the solutions to applied problems, attaching the appropriate units to an answer;
• determine asymptotes of a function by using limits; and
• determine the values of indeterminant form limits by using derivatives and L'Hopital's Rule.