Question: A function \(y=f(x)\) and values of \(x_{0}\) and \(x_{1}\) are given.

1. Find the average rate of change of \(y\) with respect to \(x\) over the interval \(\left[x_{0}, x_{1}\right]\).
2. Find the instantaneous rate of change of \(y\) with respect to \(x\) at the specified value of \(x_{0}\)
3. Find the instantaneous rate of change of \(y\) with respect to \(x\) at an arbitrary value of \(x_{0}\).
4. The average rate of change in part (a) is the slope of a certain secant line, and the instantaneous rate of change in part (b) is the slope of a certain tangent line. Sketch the graph of \(y=f(x)\) together with those two lines.

\(y=x^{3} ; x_{0}=1, x_{1}=2\)

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