Find the equation of the tangent line of $x ^ { 3 } + y ^ { 3 } = 49 ( x - y )$ at the origin.
A)y = 49x
B)y = x
C)y = 3x - 49
D)y - 49 = 3(x - y)
E)none of the above

Question

Quizplus · Accepted Answer

To find the tangent line at the origin, we first differentiate the given equation implicitly with respect to $x$. At the origin $(0,0)$, the derivative simplifies to $y' = 1$, indicating the slope of the tangent line is 1. Thus, the equation of the tangent line is $y = x$.

Find the Equation of the Tangent Line Of x3+y3=49(x−y)x ^ { 3 } + y ^ { 3 } = 49 ( x - y )x3+y3=49(x−y)

Find the Equation of the Tangent Line Of $x ^ { 3 } + y ^ { 3 } = 49 ( x - y )$