Calculus on a Parabola

1 A general equation for a parabola is \(f(x)=Ax^2+Bx+C\).

  1. Find \(f'(x)\) and \(f'(0)\)

  2. Evaluate \(\displaystyle \int_{-h}^h f(x) \, dx\)

2 Assume you have a parabola with points at \((-h, y_0)\), \((0,y_1)\), and \((h,y_2)\).

  1. Find values for \(A\), \(B\), and \(C\) in terms of \(h, y_0, y_1\) and \(y_2\)

  2. Find \(f'(x)\) and \(f'(0)\) in terms of \(h, y_0, y_1\) and \(y_2\)

  3. Evaluate \(\displaystyle \int_{-h}^h f(x) \, dx\) in terms of \(h, y_0, y_1\) and \(y_2\)