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.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.