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