The discussion revolves around a related rates problem involving a particle moving along the curve defined by y=x^1/3. The specific question is about determining the rate of change of the angle of inclination, theta, when x=8, given that x is increasing at a rate of 3 cm/s.
The conversation is active, with participants providing guidance on how to approach the problem. There is an emphasis on deriving expressions and understanding the geometric relationships involved, but no consensus has been reached on the final solution.
Participants are working within the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. There is also a hint provided regarding the approximate value of theta when x=8.
A particle is moving along the graph of y=x^1/3.
Suppose x is increasing at the rate of 3 cm/s.
At what rate is the angle of inclination, theta, changing when x=8?
[Hint: when x=8, theta approx. 0.24 rad]Well, the derivative of a constant (0.24) is 0 so that wouldn't do a whole lot of good would it?NIZBIT said:
It's a lot more helpful to find the derivative of a function rather than a number! Draw a picture, showing the "angle of inclination" and write theta as a function of x. Then find the derivative of that function with respect to x. (Do you remember that the derivative of a function is the tangent of the angle the tangent line to the graph makes with the x-axis?)
