Write a program that approximates the derivative of a given (differentiable) function f (x) at x = x0, using forward difference formula taking only 3 points having value of x as 0, 1 and 2 respectively. Using the program find the derivative of function f(x)=( x ) 5/2 at x=0.5
Sure, I'd be happy to help you with that! Let's break down the problem step by step.
Firstly, the forward difference formula for approximating the derivative is given by:
\[f'(x_0) \approx \frac{f(x_0 + h) - f(x_0)}{h},\]
where \(h\) is the step size.
In your case, you want to take three points with \(x\) values 0, 1, and __________ ___ _______ _______ ______ _____ ___.
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