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Calculus Tangent lines

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find the equation of a tangent line of

x^(1/4) + y^(1/4) = 4 at the point (16,16)

  • Calculus Tangent lines - ,

    Use implicit differentiation to find y'.
    x^(1/4)+y^(1/4)=4
    differentiate with respect to x:
    x^(-3/4)+y^(-3/4)*dy/dx=0

    dy/dx
    = -x^(-3/4)*y(3/4)
    = -x^(-3/4)*(4-x^(1/4))^3
    For x=16,
    dy/dx = -1

    Find the line that passes through (16,16) with a slope of dy/dx = -1.

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