how to find an approximate value for 4^(3/4) using one step of the secant method with x0 = 3 and x1 = 2 ?

(the actual value is about 2.8284)

any help would be greatly appreciated?

You want to find \(\displaystyle x\) such that \(\displaystyle x=4^{3/4}\) . To use the secant method you first need to rearrange this into the form: \(\displaystyle f(x)=0\). In this case:

\(\displaystyle f(x)=x^4-64\)

will suffice, now you just apply the formula.

\(\displaystyle x_{n+1}=x_n-\left[\frac{(x_n-x_{n-1})}{f(x_n)-f(x_{n-1})}\right]f(x_n)\)

CB