Chapter 13, Problem 18P

The deflection of a uniform beam subject to a linearly increasing distributed load can be computed as

$y=\frac{{\omega }_0}{120EIL}\left(-x^5+2L^2{x}^3-L^{4}x\right)$

Given that $L=600$cm, $E=50,000{\text{kN/cm}}^2$, $I=30,000{\text{cm}}^4$, and ${\omega }_0=2.5$kN/cm, determine the point of maximum deflection (a) graphically, (b) using the golden-section search until the approximate error falls below ${\epsilon }_s=1\%$ with initial guesses of $x_1=0$ and $x_l=0\text{and}{x}_u=L$