Derivative of parametric function

  • #1

Homework Statement


Find the line tangent to the point 2pi/3 when x=cost y=sqrt3 cost.
Also find the value of d2y/dx2 at the point given.


Homework Equations


I found dy/dx to be -sqrt3 sint/ -sint. I found that to be just sqrt3. This matched what my calculator told me the slope was. The equation of the tangent is y=sqrt3 x or at least I think.

I am having trouble with the second derivative. I believe that it is 0. When I applied the quotient rule to dy/dx I got sqrt3 sintcost-sqrt3 sintcost/sin2t. I then multiplied by dt/dx. Either way, the numerator is still 0.

Am I right, on the right path, or completely wrong.
 

Answers and Replies

  • #2
73
1
I think you're right. d2y/dx2 = 0
 
  • #3
Defennder
Homework Helper
2,591
5
Yes that is correct. You can get the same answer easily by noting that since dy/dx = constant. Hence d/dx (dy/dx) = 0.
 

Related Threads on Derivative of parametric function

  • Last Post
Replies
16
Views
3K
Replies
1
Views
2K
Replies
1
Views
1K
  • Last Post
Replies
6
Views
865
  • Last Post
Replies
2
Views
2K
Replies
5
Views
2K
  • Last Post
Replies
2
Views
681
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
9
Views
731
Top