forward-difference formula

Approximating a derivative from the current point and one point ahead of it.

The forward-difference formula approximates $f'(x)$ by $\dfrac{f(x+h)-f(x)}{h}$ , the slope of the secant line through $(x,f(x))$ and $(x+h,f(x+h))$ . Its truncation error is $O(h)$ : halving $h$ roughly halves the error.

Examples

For $f(x)=x^2$ at $x=1$ , $h=0.1$ : $\dfrac{f(1.1)-f(1)}{0.1}=\dfrac{1.21-1}{0.1}=2.1$ , close to but not exactly the true $f'(1)=2$ .