Using the Forward Divided Difference Method, manually solve for the approximate value of the first derivative f’(xi) at xi = 0.5 of the given function, the absolute relative true error, εt, and absolute relative approximate error, εa, using step sizes ∆x = 0.5 and ∆x = 0.25. Use five (5) decimal places in evaluating the first derivative of the function and computing for the errors. f(x) = 5x3 - cos(2x)

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A: Note:- For this problem you don't mention step size and method  (two -point , three point or five…

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A: We can find the answer in the following steps.

Q: Which functions have a negative first derivative for all x?

A: Which functions have a negative first derivative for all x?

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Q: 0,2 0,5 0,6 0,4 0,528 0,3 f(x) 0,224 0,363 0,725 0,960

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