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.