Worksheets — Set 10

Calculus BC · AP · Differentiation — Composite, Implicit, and Inverse Functions

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

Warm-up

1. Find lim(x→13) (x² − 169)/(x − 13) = ___ 2. If f(x) = 13x³ − 14x, find f′(12) = ___ 3. ∫₀^13 (14x + 1) dx = ___

_See printable PDF for diagram._

Written practice

1. Find lim(x→12) (x² − 144)/(x − 12) = ___ 2. If f(x) = 12x³ − 13x, find f′(11) = ___ 3. ∫₀^12 (13x + 1) dx = ___ 4. Find critical points of f(x) = x² − 24x + 15 ___ 5. Related rates: radius grows 11 cm/s. Find dV/dt when r = 13. ___ 6. State the meaning of f′(a) in context. ___ 7. Find lim(x→15) (x² − 225)/(x − 15) = ___ 8. If f(x) = 15x³ − 16x, find f′(14) = ___

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More written practice

1. ∫₀^15 (16x + 1) dx = ___ 2. Find critical points of f(x) = x² − 30x + 18 ___ 3. Related rates: radius grows 14 cm/s. Find dV/dt when r = 16. ___ 4. Find lim(x→18) (x² − 324)/(x − 18) = ___ 5. If f(x) = 18x³ − 19x, find f′(17) = ___ 6. ∫₀^18 (19x + 1) dx = ___

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Patterns and rules

1. Find lim(x→29) (x² − 841)/(x − 29) = ___ 2. If f(x) = 29x³ − 30x, find f′(28) = ___ 3. ∫₀^29 (30x + 1) dx = ___

_See printable PDF for diagram._

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Parent tip: Sketch graphs to check signs and behavior