Worksheets — Set 9

Calculus BC · AP · Contextual Applications of Differentiation

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

Warm-up

1. Find lim(x→12) (x² − 144)/(x − 12) = ___ 2. If f(x) = 12x³ − 13x, find f′(11) = ___ 3. ∫₀^12 (13x + 1) dx = ___

_See printable PDF for diagram._

Written practice

1. Find lim(x→11) (x² − 121)/(x − 11) = ___ 2. If f(x) = 11x³ − 12x, find f′(10) = ___ 3. ∫₀^11 (12x + 1) dx = ___ 4. Find critical points of f(x) = x² − 22x + 14 ___ 5. Related rates: radius grows 10 cm/s. Find dV/dt when r = 12. ___ 6. State the meaning of f′(a) in context. ___ 7. Find lim(x→14) (x² − 196)/(x − 14) = ___ 8. If f(x) = 14x³ − 15x, find f′(13) = ___

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More written practice

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

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Patterns and rules

1. Find lim(x→28) (x² − 784)/(x − 28) = ___ 2. If f(x) = 28x³ − 29x, find f′(27) = ___ 3. ∫₀^28 (29x + 1) dx = ___

_See printable PDF for diagram._

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Parent tip: Sketch graphs to check signs and behavior