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

Tangents, normals and gradient with technology Problem set A Answers

Skills

    1. (a) \(y=4.77x-6.77\)
    2. (b) \(y=-0.600x+2.80\)
    3. (c) \(y=5.55x-8.64\)
    1. (a) \(y=-6.00x+27.0\)
    2. (b) \(y=-0.400x+13.6\)
    1. (a) \(y=-2.00x+6.30\)
    2. (b) \(y=-0.250x+3.00\)
    1. (a) x = 22.0
    2. (b) x = 0.805
    1. (a) x = −3.00 or x = 1.00
    2. (b) x = 1.78
    1. (a) \(\frac{dy}{dx}=4x^{3}+2\)
    2. (b) m = 2
    3. (c) \(y=-\frac{1}{2}x\)
    1. (a) \(f'(x)=8x^{3}-3x^{-2}\)
    2. (b) m = 5
    3. (c) \(y=5x\), which passes through \((0, 0)\)

In context

    1. (a) \(F=1.77t-1.33\)
    2. (b) t = 1.47

Stretch

    1. (a) x = 2.52
    2. (b) \(y=-2.00x+10.1\)

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