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4. For the curve with y = -2x3 + x - 6, find:




(b.) the gradient at the point (-1, -5)






(c.) the equation of the tangent line at the point (-1, -5).

  • math -

    y = -2x^3 + x - 6
    dy/dx = -6x + 1

    at (-1,-5), dy/dx = -6(-1) + 1 = 7

    so y = -7x + b
    at (-1,-5)
    -5 = -7(-1) + b
    b = -12

    equation of tangent is y = -7x - 12

  • math -

    y = -2x^3 + x - 6
    dy/dx = -6x + 1

    at (-1,-5), dy/dx = -6(-1) + 1 = 7

    so y = -7x + b
    at (-1,-5)
    -5 = -7(-1) + b
    b = -12

    equation of tangent is y = -7x - 12

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