Worksheets — Set 4

Calculus I · Applications of derivatives

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

Warm-up

1. Find lim(x→7) (x² − 49)/(x − 7) = ___ 2. If f(x) = 7x³ − 8x, find f′(6) = ___ 3. ∫₀^7 (8x + 1) dx = ___

_See printable PDF for diagram._

Written practice

1. Find lim(x→6) (x² − 36)/(x − 6) = ___ 2. If f(x) = 6x³ − 7x, find f′(5) = ___ 3. ∫₀^6 (7x + 1) dx = ___ 4. Find critical points of f(x) = x² − 12x + 9 ___ 5. Related rates: radius grows 5 cm/s. Find dV/dt when r = 7. ___ 6. State the meaning of f′(a) in context. ___ 7. Find lim(x→9) (x² − 81)/(x − 9) = ___ 8. If f(x) = 9x³ − 10x, find f′(8) = ___

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More written practice

1. ∫₀^9 (10x + 1) dx = ___ 2. Find critical points of f(x) = x² − 18x + 12 ___ 3. Related rates: radius grows 8 cm/s. Find dV/dt when r = 10. ___ 4. Find lim(x→12) (x² − 144)/(x − 12) = ___ 5. If f(x) = 12x³ − 13x, find f′(11) = ___ 6. ∫₀^12 (13x + 1) dx = ___

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Patterns and rules

1. Find lim(x→23) (x² − 529)/(x − 23) = ___ 2. If f(x) = 23x³ − 24x, find f′(22) = ___ 3. ∫₀^23 (24x + 1) dx = ___

_See printable PDF for diagram._

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Parent tip: Sketch graphs to check signs and behavior