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IB Mathematics: Applications and Interpretation HL · 12.9: Differentiation · 12.9.9

Tangents, normals and gradient with technology Problem set B Answers

Skills

    1. (a) \(y=3.40x-6.59\)
    2. (b) \(y=-0.960x+3.12\)
    3. (c) \(y=9.89x-10.8\)
    1. (a) \(y=-6.00x+15.0\)
    2. (b) \(y=-0.225x+30.0\)
    1. (a) \(y=-4.00x+18.8\)
    2. (b) \(y=-0.333x+2.00\)
    1. (a) x = 4.25
    2. (b) x = 0.462
    1. (a) x = −3.41 or x = −0.586
    2. (b) x = 2.00
    1. (a) \(\frac{dy}{dx}=4x^{3}-5\)
    2. (b) m = −5
    3. (c) \(y=\frac{1}{5}x\)
    1. (a) \(f'(x)=5x^{4}-2x^{-2}\)
    2. (b) m = 3
    3. (c) \(y=3x\), which passes through \((0, 0)\)

In context

    1. (a) \(d=1.64t-0.250\)
    2. (b) t = 1.97

Stretch

    1. (a) x = 3.30
    2. (b) \(y=-2.00x+13.2\)

jmaths.xyz · AI HL · 12.9.9 Tangents, normals and gradient with technology