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[Solved] Let f(x)=x(1-2 x). Find the average rate of change of f(x) with respect to x as x changes from x=0 to x=1/2. Use calculus to find the instantaneous

Question: Let \(f(x)=x(1-2 x)\).

  1. Find the average rate of change of \(f(x)\) with respect to \(x\) as \(x\) changes from \(x=0\) to \(x=\frac{1}{2}\).
  2. Use calculus to find the instantaneous rate of change of \(f(x)\) at \(x=0\) and compare with the average rate found in part (a).

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