Common Mistakes
Calculus BC · AP · Analytical Applications of Differentiation
Focus
Using the Candidates Test to Determine Absolute (Global) Extrema
This topic is assessed on the AP Exam.
Frequent mistakes
### 1. Chain rule omission
What it looks/sounds like: Inner derivative is dropped on composite functions.
Why it happens: Only the outer rule is applied.
How to fix: Write g′(x) explicitly when differentiating f(g(x)).
### 2. Critical point = extremum
What it looks/sounds like: f′(a)=0 is claimed as max/min without a test.
Why it happens: Critical points are equated with extrema.
How to fix: Use first or second derivative test or compare endpoints.
### 3. MVT/EVT hypotheses skipped
What it looks/sounds like: Theorem is cited without continuity/differentiability on the interval.
Why it happens: Theorem names are used as magic words.
How to fix: List hypotheses, then apply the conclusion.
### 4. Correct work, wrong question
What it looks/sounds like: The algebra is fine but answers a different quantity than the stem asks for.
Why it happens: Attention locks onto the first operation instead of the final ask.
How to fix: Underline the final question; after solving, verify the boxed answer matches it.
### 5. Notation and justification gaps
What it looks/sounds like: Missing units, limit language, or ‘because’ statements AP graders expect.
Why it happens: Notation is treated as decoration rather than part of the score.
How to fix: Add one justification phrase per major step (definition, theorem, or rule).
How to avoid them
1. Use sign charts for f′ and f″. 2. Check endpoints on closed intervals. 3. Name the theorem you are using.
Quick self-check
- [ ] Can justify an extreme value
- [ ] Can read f′ sign chart
- [ ] Can state MVT/EVT conditions