Worksheets — Set 5

Calculus BC · AP · Analytical Applications of Differentiation

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

Warm-up

1. Find lim(x→8) (x² − 64)/(x − 8) = ___ 2. If f(x) = 8x³ − 9x, find f′(7) = ___ 3. ∫₀^8 (9x + 1) dx = ___

_See printable PDF for diagram._

Written practice

1. Find lim(x→7) (x² − 49)/(x − 7) = ___ 2. If f(x) = 7x³ − 8x, find f′(6) = ___ 3. ∫₀^7 (8x + 1) dx = ___ 4. Find critical points of f(x) = x² − 14x + 10 ___ 5. Related rates: radius grows 6 cm/s. Find dV/dt when r = 8. ___ 6. State the meaning of f′(a) in context. ___ 7. Find lim(x→10) (x² − 100)/(x − 10) = ___ 8. If f(x) = 10x³ − 11x, find f′(9) = ___

___________________________ ___________________________ ___________________________ ___________________________

More written practice

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

___________________________ ___________________________ ___________________________ ___________________________ ___________________________

Patterns and rules

1. Find lim(x→24) (x² − 576)/(x − 24) = ___ 2. If f(x) = 24x³ − 25x, find f′(23) = ___ 3. ∫₀^24 (25x + 1) dx = ___

_See printable PDF for diagram._

___________________________ ___________________________ ___________________________ ___________________________

Parent tip: Sketch graphs to check signs and behavior