Worksheets — Set 2

Calculus AB · AP · Differentiation — Composite, Implicit, and Inverse Functions

Print and write your answers. Use diagrams to show thinking.

Warm-up

1. Find lim(x→5) (x² − 25)/(x − 5) = ___ 2. If f(x) = 5x³ − 6x, find f′(4) = ___ 3. ∫₀^5 (6x + 1) dx = ___

_See printable PDF for diagram._

Written practice

1. Find lim(x→4) (x² − 16)/(x − 4) = ___ 2. If f(x) = 4x³ − 5x, find f′(3) = ___ 3. ∫₀^4 (5x + 1) dx = ___ 4. Find critical points of f(x) = x² − 8x + 7 ___ 5. Related rates: radius grows 3 cm/s. Find dV/dt when r = 5. ___ 6. State the meaning of f′(a) in context. ___ 7. Find lim(x→7) (x² − 49)/(x − 7) = ___ 8. If f(x) = 7x³ − 8x, find f′(6) = ___

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More written practice

1. ∫₀^7 (8x + 1) dx = ___ 2. Find critical points of f(x) = x² − 14x + 10 ___ 3. Related rates: radius grows 6 cm/s. Find dV/dt when r = 8. ___ 4. Find lim(x→10) (x² − 100)/(x − 10) = ___ 5. If f(x) = 10x³ − 11x, find f′(9) = ___ 6. ∫₀^10 (11x + 1) dx = ___

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Patterns and rules

1. Find lim(x→21) (x² − 441)/(x − 21) = ___ 2. If f(x) = 21x³ − 22x, find f′(20) = ___ 3. ∫₀^21 (22x + 1) dx = ___

_See printable PDF for diagram._

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Parent tip: Sketch graphs to check signs and behavior