Worksheets — Set 7

Calculus I · Applications of derivatives

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

Warm-up

1. Find lim(x→10) (x² − 100)/(x − 10) = ___ 2. If f(x) = 10x³ − 11x, find f′(9) = ___ 3. ∫₀^10 (11x + 1) dx = ___

_See printable PDF for diagram._

Written practice

1. Find lim(x→9) (x² − 81)/(x − 9) = ___ 2. If f(x) = 9x³ − 10x, find f′(8) = ___ 3. ∫₀^9 (10x + 1) dx = ___ 4. Find critical points of f(x) = x² − 18x + 12 ___ 5. Related rates: radius grows 8 cm/s. Find dV/dt when r = 10. ___ 6. State the meaning of f′(a) in context. ___ 7. Find lim(x→12) (x² − 144)/(x − 12) = ___ 8. If f(x) = 12x³ − 13x, find f′(11) = ___

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More written practice

1. ∫₀^12 (13x + 1) dx = ___ 2. Find critical points of f(x) = x² − 24x + 15 ___ 3. Related rates: radius grows 11 cm/s. Find dV/dt when r = 13. ___ 4. Find lim(x→15) (x² − 225)/(x − 15) = ___ 5. If f(x) = 15x³ − 16x, find f′(14) = ___ 6. ∫₀^15 (16x + 1) dx = ___

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Patterns and rules

1. Find lim(x→26) (x² − 676)/(x − 26) = ___ 2. If f(x) = 26x³ − 27x, find f′(25) = ___ 3. ∫₀^26 (27x + 1) dx = ___

_See printable PDF for diagram._

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Parent tip: Sketch graphs to check signs and behavior