Practice: Calculus and Trigonometry

Level pending

Let \(y_1\) and \(y_2\) be lines tangent to the graph of \(f(x)=x^{2}-8x+3\) that make a \(60^{\circ}\) angle with respect to the line \(y=\frac{1}{2}x\). If the lines intersect \(f\) at \(x=x_1\) and \(x=x_2\), what is the arithmetic mean of \(x_1\) and \(x_2\)?

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