The discussion focuses on finding the equation of the tangent line to the curve defined by the equation \(y^2 = x(x-3)^2\) at the point (3,0). Participants emphasize the necessity of using implicit differentiation and the product rule for accurate calculations. The correct derivative is derived as \(dy/dx = \frac{2x(x-3)}{2y}\), highlighting the importance of applying both the product and chain rules in the differentiation process. The conversation also touches on the need for further exploration of horizontal tangents in related equations.
PREREQUISITESStudents studying calculus, particularly those focusing on implicit differentiation and tangent line calculations, as well as educators looking for examples of teaching these concepts effectively.
You have a mistake above. x * (x - 3)2 is a product, so the product rule is needed.Torshi said:Homework Statement
Find the equation of y^2=x(x-3)^2 of tangent line at (3,0)
Homework Equations
Given above.
I think implicit differentiation is involved or no since there is no xy's on the same side?
The Attempt at a Solution
Anyways...
My attempt:
2ydy/dx = x*2(x-3)*1
Torshi said:2ydy/dx=2x(x-3)
dy/dx= 2x(x-3)/2y
dy/dx= 2x^2-6x/2y
Doesn't seem right.