Let \( C_{1} \) and \( C_{2} \) be the graphs of functions \( y=x^{2} \) and \( y=2 x \), \( 0 \... VIDEO
Let \( C_{1} \) and \( C_{2} \) be the graphs of functions \( y=x^{2} \) and \( y=2 x \), \( 0 \leq x \leq 1 \), respectively. Let \( C_{3} \) be the graph of a function \( y \) \( =f(x), 0 \leq x \leq 1, f(0)=0 \). For a point \( P \) on \( C_{1} \), let the lines through \( P \), parallel to the axes, meet \( C_{2} \) and \( C_{3} \) at \( Q \) and \( R \) respectively (see figure). If for every position of \( P\left(\right. \) on \( C_{1} \) ) the areas of the shaded regions \( O P Q \) and \( O R P \) are equal, then determine \( f(x) \).https://bit.ly/YTAI_PWAP https://www.pw.live
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