Find the equation of y^2=x(x-3)^2 of tangent line at (3,0)

[Torshi]

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
2ydy/dx=2x(x-3)
dy/dx= 2x(x-3)/2y
dy/dx= 2x^2-6x/2y


Doesn't seem right.

 

[Torshi]

Another problem" Determine (x,y) location(s) where the graph of y^4 = y^2-x^2 has horizontal tangents

I got the answer dy/dx = -2x/4y^3-2y

I don't know how to calculate x and y positions? I just found the implicit differentiation

 

[Mark44]

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

You have a mistake above. x * (x - 3)² is a product, so the product rule is needed.

After you use the product rule, you will need to use the chain rule.

2ydy/dx=2x(x-3)
dy/dx= 2x(x-3)/2y
dy/dx= 2x^2-6x/2y


Doesn't seem right.