Worksheets — Set 12

Calculus BC · AP · Analytical Applications of Differentiation

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

Warm-up

1. Find lim(x→15) (x² − 225)/(x − 15) = ___ 2. If f(x) = 15x³ − 16x, find f′(14) = ___ 3. ∫₀^15 (16x + 1) dx = ___

_See printable PDF for diagram._

Written practice

1. Find lim(x→14) (x² − 196)/(x − 14) = ___ 2. If f(x) = 14x³ − 15x, find f′(13) = ___ 3. ∫₀^14 (15x + 1) dx = ___ 4. Find critical points of f(x) = x² − 28x + 17 ___ 5. Related rates: radius grows 13 cm/s. Find dV/dt when r = 15. ___ 6. State the meaning of f′(a) in context. ___ 7. Find lim(x→17) (x² − 289)/(x − 17) = ___ 8. If f(x) = 17x³ − 18x, find f′(16) = ___

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More written practice

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

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Patterns and rules

1. Find lim(x→31) (x² − 961)/(x − 31) = ___ 2. If f(x) = 31x³ − 32x, find f′(30) = ___ 3. ∫₀^31 (32x + 1) dx = ___

_See printable PDF for diagram._

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Parent tip: Sketch graphs to check signs and behavior