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IB Mathematics: Applications and Interpretation HL · 12.9: Differentiation · 12.9.13

Optimisation in context Problem set B Answers

Skills

    1. (a) t = 11 hours
    2. (b) 61.5 customers per hour
    1. (a) v = 12 knots
    2. (b) 216 dollars per hour
    1. (a) f = 0.333
    2. (b) 1.78 hundred pounds
    1. (a) \(h=\frac{864-6x^2}{8x}\)
    2. (b) \(V=324x-2.25x^3\)
    3. (c) V = 1500 cm³ when x = 6.93
    1. (a) \(A=84x-2x^2\)
    2. (b) A = 882 m² when x = 21
    1. (a) \(54-2x\) and \(30-2x\)
    2. (b) \(V=x(54-2x)(30-2x)\), \(0<x<15\)
    3. (c) V = 4540 cm³ when x = 6.19

In context

    1. (a) t = 15 seconds
    2. (b) 33.8 m/s
    1. (a) \(h=\frac{4000}{x^2}\)
    2. (b) \(S=x^2+\frac{16000}{x}\)
    3. (c) S = 1200 cm² when x = 20
    1. (a) Price \(=10+0.5x\) euros; number sold \(=400-15x\)
    2. (b) \(P=(8+0.5x)(400-15x)\)
    3. (c) Profit €3412.50 at a price of €12.50 (x = 5)
    1. (a) \(L=\frac{160-\pi w}{2}\)
    2. (b) \(A=\frac{w(160-\pi w)}{2}\)
    3. (c) A = 1020 m² when w = 25.5

Stretch

    1. (a) \(V=450r-\pi r^3\)
    2. (b) V = 2070 cm³ when r = 6.91
    1. (a) \(C=20x+\frac{3600}{x}\)
    2. (b) £536.66 when x = 13.4 m and y = 33.5 m

jmaths.xyz · AI HL · 12.9.13 Optimisation in context