Final answer:
To determine the arc length of the given curve from x=0 to x=16, one must take the integral of the square root of 1 plus the squared derivative of the curve, integrated from a to b, where a and b are the interval limits.
Step-by-step explanation:
The length of the arc of the curve y = \frac{34}{2} (4x-1)^\frac{2}{3} from x = 0 to x = 16 can be found using calculus, specifically by integrating the formula for arc length. The formula for the arc length of a function y = f(x), given that f'(x) is continuous on [a, b], is given by:
L = \int_{a}^{b} \sqrt{1 + [f'(x)]^2} dx
We would calculate the derivative of the given function, square it, add one, then take the square root and integrate the function from x = 0 to x = 16. In this case, the calculation is not straightforward and would typically require the use of integration techniques taught in Advanced Placement (AP) Calculus or college level calculus courses.