MATH 142 - Exam 2 Questions with
complete solution 2026
Critical value(s) - correct answer ✔A number c in the domain of f such that either f'(c)=0 or f'(c) DNE
The First Derivative Test - correct answer ✔This test finds local maximums, local minimums, and where
the graph is increasing and decreasing
Concavity Test - correct answer ✔This test finds concave upward, concave downward, and inflection
points
The Second Derivative Test - correct answer ✔This test uses the 2nd derivative to find the local/relative
extrema
Closed Interval Method - correct answer ✔If the interval is continuous and closed, we use this to find
the absolute maximum and/or the absolute minimum
1st Derivative Test (Optimization) - correct answer ✔If the interval is open and there's only one critical
value, we use this to fine the absolute extrema
Extreme Value Theorem - correct answer ✔If f is continuous on closed interval [a,b], then f has an
absolute max and min
complete solution 2026
Critical value(s) - correct answer ✔A number c in the domain of f such that either f'(c)=0 or f'(c) DNE
The First Derivative Test - correct answer ✔This test finds local maximums, local minimums, and where
the graph is increasing and decreasing
Concavity Test - correct answer ✔This test finds concave upward, concave downward, and inflection
points
The Second Derivative Test - correct answer ✔This test uses the 2nd derivative to find the local/relative
extrema
Closed Interval Method - correct answer ✔If the interval is continuous and closed, we use this to find
the absolute maximum and/or the absolute minimum
1st Derivative Test (Optimization) - correct answer ✔If the interval is open and there's only one critical
value, we use this to fine the absolute extrema
Extreme Value Theorem - correct answer ✔If f is continuous on closed interval [a,b], then f has an
absolute max and min
