Question

Find dy/dx |_(x = 3, y = 2) by implicit differentiation of x^4+y^4 = 97

What is the geometric meaning of dy/dx |_(x = 3, y = 2) ?

Answer 1

geometric meaning of dy/dx: the slope of a tangent line at (3,2) on the circle

Answer 2

Circle? I suppose.

Answer 3

actually nvm, it's not a circle

Answer 4

\[x^4+y^4=97\]
\[4x^3+4y^3\frac{ dy }{ dx }=0,\frac{ dy }{ dx }=\frac{ -4x^3 }{ 4y^3 }=\frac{ -x^3 }{y^3 }\]
plug x=3,y=2 and get the value of dy/dx