9. Roller bearings are subject to fatigue failure caused by large contact loads F. The problem

of finding the location of maximum stress along the x-axis can be shown to be equivalent

to maximizing the function:

0.4

√1 + x²

+ x² (1

Find x (to at least 8-digit accuracy) that maximizes f(x) employing the following numerical

optimization methods: secant, optm_golden and fminbnd. Choose an initial guess/initial

interval based on a plot of f(x). Hint: optm_golden and fminbdn can only locate a

minimum, but we may use if to locate a maximum if we multiply f(x) by -1.

f(x) = x +-

0.4

1+x²