Exam Strategy
Readiness Check
- State degree and leading coefficient from a polynomial form.
- Locate/describe local vs global extrema from a graph or description.
- Use: between two real zeros there is at least one local extremum.
- Recall even-degree polynomials have a global max or min.
- Describe inflection as change in how the rate of change is changing (concavity).
Before the Exam
1. Sketch cubics with two turns; label local max/min. 2. Sketch even-degree graphs with a global min (upward) vs global max (downward). 3. Practice "between zeros" reasoning with factored polynomials. 4. Contrast: turning point (extremum) vs inflection (concavity change).
During Multiple Choice
- Read whether the stem asks local or global.
- Even degree + positive leading coefficient → global min (opens up end behavior).
- Inflection language: rate of change increasing ↔ decreasing, not just "a high point."
During Free Response
1. Identify degree / leading coefficient if needed. 2. Name intervals of increase/decrease, then the switch points as local extrema. 3. Justify global extrema with even-degree CED language when relevant. 4. For inflection, explicitly mention change in the rate of change / concavity.
Common Traps
- Calling every wiggle a global extremum.
- Thinking odd-degree polynomials must have a global max and min (they need not).
- Mixing zeros with extrema locations (extrema lie between zeros, not necessarily at zeros).
60-Second Checklist
- Local vs global clear?
- Even-degree global claim justified?
- Between-zeros theorem used correctly?
- Inflection = concavity / rate-of-rate change?