Asked by kevin
                 find the equation of a tangent line of    
x^(1/4) + y^(1/4) = 4 at the point (16,16)
            
        x^(1/4) + y^(1/4) = 4 at the point (16,16)
Answers
                    Answered by
            MathMate
            
    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.
    
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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