Exam Strategy

Calculus BC · AP · Analytical Applications of Differentiation

CED focus

Determining Intervals on Which a Function Is Increasing or Decreasing

This topic is assessed on the AP Exam.

Multiple-choice tips

• Identify whether the stem tests a definition, rule, or application.
• On graph MC, decide whether the question is about f, f′, or f″.
• Eliminate extrema claims without endpoint or critical-point checks.
• Watch MVT/EVT hypothesis language in justification choices.
• Use sign charts mentally for increasing/decreasing MC.

Free-response tips

• Label f′(a) meaning in context; show the rule that justifies each step.
• Name the theorem (MVT, EVT, first/second derivative test) you use.
• Show a sign chart or number line for extrema/concavity arguments.
• Check endpoints on a closed interval for absolute extrema.
• Connect f′ and f″ conclusions to the graph of f in words.

Common traps

• Mixing average rate over an interval with instantaneous rate at a point
• Claiming a critical point is a max/min without a test
• Applying MVT without continuity/differentiability on the interval
• Confusing f′ graph with f graph

Quick checklist

• [ ] Can justify an extreme value with a test or endpoints
• [ ] Can read increasing/decreasing from f′ sign
• [ ] Can state MVT/EVT hypotheses when using them