Worksheets — Set 19

Calculus BC · AP · Contextual Applications of Differentiation

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

Warm-up

1. Find lim(x→22) (x² − 484)/(x − 22) = ___ 2. If f(x) = 22x³ − 23x, find f′(21) = ___ 3. ∫₀^22 (23x + 1) dx = ___

_See printable PDF for diagram._

Written practice

1. Find lim(x→21) (x² − 441)/(x − 21) = ___ 2. If f(x) = 21x³ − 22x, find f′(20) = ___ 3. ∫₀^21 (22x + 1) dx = ___ 4. Find critical points of f(x) = x² − 42x + 24 ___ 5. Related rates: radius grows 20 cm/s. Find dV/dt when r = 22. ___ 6. State the meaning of f′(a) in context. ___ 7. Find lim(x→24) (x² − 576)/(x − 24) = ___ 8. If f(x) = 24x³ − 25x, find f′(23) = ___

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More written practice

1. ∫₀^24 (25x + 1) dx = ___ 2. Find critical points of f(x) = x² − 48x + 27 ___ 3. Related rates: radius grows 23 cm/s. Find dV/dt when r = 25. ___ 4. Find lim(x→27) (x² − 729)/(x − 27) = ___ 5. If f(x) = 27x³ − 28x, find f′(26) = ___ 6. ∫₀^27 (28x + 1) dx = ___

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Patterns and rules

1. Find lim(x→38) (x² − 1444)/(x − 38) = ___ 2. If f(x) = 38x³ − 39x, find f′(37) = ___ 3. ∫₀^38 (39x + 1) dx = ___

_See printable PDF for diagram._

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Stretch

1. Find lim(x→46) (x² − 2116)/(x − 46) = ___ 2. If f(x) = 46x³ − 47x, find f′(45) = ___

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Parent tip: Sketch graphs to check signs and behavior