2-dimensional bowl

Calculus Level 3

The ends \(A\) and \(B\) of a rod of length of \(\sqrt{5}\) are sliding along the curve \(y=2x^2\). Let \(x_A\) and \(x_B\) be the \(x\)-coordinates of the ends. At the moment when \(A\) is at \((0,0)\) and \(B\) is at \((1,2)\). Find the value of the derivative \(\dfrac{dx_B}{dx_A}\).

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