(Solved): The arc length function for a curve \( y=f(x) \), where \( f \) is an increasing function, is \( s ...

The arc length function for a curve \( y=f(x) \), where \( f \) is an increasing function, is \( s(x)=\int_{0}^{x} \sqrt{7 t+10} d t \). (a) If \( f \) has \( y \)-intercept 7 , find an equation for \( f \). \[ f(x)=\frac{2}{21} \cdot(7 x+9)^{\left(\frac{3}{2}\right)}+\frac{31}{7} \] (b) What point on the graph of \( f \) is 4 units along the curve from the \( y \)-intercept? State your answer rounded to 3 decimal places.