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

Optimisation in context Problem set A Answers

Skills

    1. (a) t = 12 hours
    2. (b) 25.2 watts
    1. (a) v = 20 km/h
    2. (b) 12 euros per km
    1. (a) s = 0.333
    2. (b) 4.44 thousand euros
    1. (a) \(h=\frac{540-4x^2}{6x}\)
    2. (b) \(V=180x-\frac{4}{3}x^3\)
    3. (c) V = 805 cm³ when x = 6.71
    1. (a) \(A=160x-2x^2\)
    2. (b) A = 3200 m² when x = 40
    1. (a) \(60-2x\) and \(36-2x\)
    2. (b) \(V=x(60-2x)(36-2x)\), \(0<x<18\)
    3. (c) V = 7090 cm³ when x = 7.28

In context

    1. (a) d = 20 hundred metres
    2. (b) 40 m³/s
    1. (a) \(h=\frac{32}{x^2}\)
    2. (b) \(S=x^2+\frac{128}{x}\)
    3. (c) S = 48 m² when x = 4
    1. (a) Price \(=3+0.1x\) euros; number sold \(=250-6x\)
    2. (b) \(P=(2+0.1x)(250-6x)\)
    3. (c) Profit €570.40 at a price of €4.10 (x = 11)
    1. (a) \(L=\frac{300-\pi w}{2}\)
    2. (b) \(A=\frac{w(300-\pi w)}{2}\)
    3. (c) A = 3580 m² when w = 47.7

Stretch

    1. (a) \(V=300r-\pi r^3\)
    2. (b) V = 1130 cm³ when r = 5.64
    1. (a) \(C=30x+\frac{9600}{x}\)
    2. (b) €1073.31 when x = 17.9 m and y = 44.7 m

jmaths.xyz · AI SL · 12.9.13 Optimisation in context