Chapter 8.1, Problem 38E

The arc length function for a curve y = f(x), where f is an increasing function, is $s\left(x\right)={\displaystyle {\int }_0^x\sqrt{3t+5}dt}$.

(a) If f has y-intercept 2, find an equation for f.

(b) What point on the graph of f is 3 units along the curve from the y-intercept? State your answer rounded to 3 decimal places.