Chapter 6, Problem 12P

Given

$f\left(x\right)=-2x^6-1.5x^4+10x+2$

Use a root location technique to determine the maximum of this function. Perform iterations until the approximate relative error falls below 5%. If you use a bracketing method, initial guesses of $x_l=0\text{ and }{x}_u=1$. If you use the Newton-Raphson or the modified secant method, use initial of $x_{i-1}=0\text{ and }{x}_i=1$. Assuming that convergence is not an issue, choose the technique that is best suited to this problem. Justify your choice.