cal3

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Using the chain rule, find the min and max points and their values of the composite function defined by:
z= x^2 + y^2, x=sin(2t), y=cos(t)

  • cal3 -

    z = x^2 + y^2
    dz/dt = 2x dx/dt + 2y dy/dt
    = 2sin(2t) * 2cos(2t) + 2cos(t) * (-sin(t))
    = 4cos(4t) - sin(2t)

    for dz/dt=0, check wolframalpha and enter

    solve 4cos(4t) - sin(2t) = 0

  • cal3 -

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