Find the rate of change of the distance between the origin and a moving point on the graph of
y = x^2 + 1 It dx/Dr = 2 cm/second
My work:
I proceeded taking the implicit derivative of the given function to find dy/dt.
dy/dt = 2x* dx/dt
dy/dt = 2x* (2) and the I plugged x = 0 from the origin value for x.
dy/dt = 2(0)* (0)
dy/dt = 0...My Answer.
Book's Answer:
2(2x^3+3x)/sqrt(x^4+3x^2+1)
My Answer is zero and the book's answer is a crazy rational function.
Can someone answer this question?
Sorry, just a little joke.
The problem is asking about how fast the distance is changing between a point on the graph and the origin. So say we have a point on the graph (x, y). What is the distance between that point and the origin? Once you get that you can take your derivative. (And recall that y = x^2 - 1 before you differentiate.)
-Dan
This is what I did:
(1) I used the distance formula for points to find d.
d = sqrt{(x-0)^2 + (x^2-1-0)}
d = sqrt{x^4-2x^2+1}
(2) I then differentiated implicitly and found dr/dt to be
[2x(2x^2-1)]/sqrt{x^4-2x^2+1}
It is not correct.