Exam Strategy

Calculus BC · AP · Differentiation — Definition and Fundamental Properties

CED focus

Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist

This topic is assessed on the AP Exam.

Multiple-choice tips

• Ask whether the limit is one-sided, two-sided, or DNE before computing.
• Separate average rate vs instantaneous rate in the stem.
• Eliminate derivative rules misapplied to products/quotients.
• Check units on rate answers in context MC.
• Use difference quotient structure when a definition is tested.

Free-response tips

• Use ‘approaches’ language; cite IVT or continuity when justifying.
• Show the limit definition when asked, then connect to a shortcut rule.
• Label what f′(a) means in context (velocity, marginal cost, slope).
• Show each differentiation rule step; do not skip the chain rule inner derivative.
• State units on derivative answers in applied FRQs.

Common traps

• Equating lim f(x) as x→a with f(a) when a hole exists
• Confusing average and instantaneous rate
• Forgetting +C only when it is an indefinite integral (not here)
• Applying the power rule to a product without product rule

Quick checklist

• [ ] Can state the derivative as a limit in words
• [ ] Can compute f′(a) with correct notation
• [ ] Can interpret a derivative in context with units