A particle moves along the curve `y=x^2+2xdot` At what point(s) on the curve are the `x` and `y` coordinates of the particle changing at the same rate?

Explanation

To solve the problem of finding the point(s) on the curve \( y = x^2 + 2x \) where the \( x \) and \( y \) coordinates of the particle are changing at the same rate, we will follow these steps:

### Step 1: Set up the relationship
We know that the rates of change of \( x \) and \( y \) with respect to time \( t \) are given by:
\[ \frac{dx}{dt} = \frac{dy}{dt} \]

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