# secant method

#### doresa

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?

#### CaptainBlack

MHF Hall of Fame
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

doresa