Worksheets — Set 15

Calculus BC · AP · Contextual Applications of Differentiation

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

Warm-up

1. Find lim(x→18) (x² − 324)/(x − 18) = ___ 2. If f(x) = 18x³ − 19x, find f′(17) = ___ 3. ∫₀^18 (19x + 1) dx = ___

_See printable PDF for diagram._

Written practice

1. Find lim(x→17) (x² − 289)/(x − 17) = ___ 2. If f(x) = 17x³ − 18x, find f′(16) = ___ 3. ∫₀^17 (18x + 1) dx = ___ 4. Find critical points of f(x) = x² − 34x + 20 ___ 5. Related rates: radius grows 16 cm/s. Find dV/dt when r = 18. ___ 6. State the meaning of f′(a) in context. ___ 7. Find lim(x→20) (x² − 400)/(x − 20) = ___ 8. If f(x) = 20x³ − 21x, find f′(19) = ___

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More written practice

1. ∫₀^20 (21x + 1) dx = ___ 2. Find critical points of f(x) = x² − 40x + 23 ___ 3. Related rates: radius grows 19 cm/s. Find dV/dt when r = 21. ___ 4. Find lim(x→23) (x² − 529)/(x − 23) = ___ 5. If f(x) = 23x³ − 24x, find f′(22) = ___ 6. ∫₀^23 (24x + 1) dx = ___

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Patterns and rules

1. Find lim(x→34) (x² − 1156)/(x − 34) = ___ 2. If f(x) = 34x³ − 35x, find f′(33) = ___ 3. ∫₀^34 (35x + 1) dx = ___

_See printable PDF for diagram._

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Parent tip: Sketch graphs to check signs and behavior