Worksheets — Set 8

Calculus BC · AP · Contextual Applications of Differentiation

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

Warm-up

1. Find lim(x→11) (x² − 121)/(x − 11) = ___ 2. If f(x) = 11x³ − 12x, find f′(10) = ___ 3. ∫₀^11 (12x + 1) dx = ___

_See printable PDF for diagram._

Written practice

1. Find lim(x→10) (x² − 100)/(x − 10) = ___ 2. If f(x) = 10x³ − 11x, find f′(9) = ___ 3. ∫₀^10 (11x + 1) dx = ___ 4. Find critical points of f(x) = x² − 20x + 13 ___ 5. Related rates: radius grows 9 cm/s. Find dV/dt when r = 11. ___ 6. State the meaning of f′(a) in context. ___ 7. Find lim(x→13) (x² − 169)/(x − 13) = ___ 8. If f(x) = 13x³ − 14x, find f′(12) = ___

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More written practice

1. ∫₀^13 (14x + 1) dx = ___ 2. Find critical points of f(x) = x² − 26x + 16 ___ 3. Related rates: radius grows 12 cm/s. Find dV/dt when r = 14. ___ 4. Find lim(x→16) (x² − 256)/(x − 16) = ___ 5. If f(x) = 16x³ − 17x, find f′(15) = ___ 6. ∫₀^16 (17x + 1) dx = ___

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Patterns and rules

1. Find lim(x→27) (x² − 729)/(x − 27) = ___ 2. If f(x) = 27x³ − 28x, find f′(26) = ___ 3. ∫₀^27 (28x + 1) dx = ___

_See printable PDF for diagram._

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Parent tip: Sketch graphs to check signs and behavior