Find $ x_3 \ $ using iteration method

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Answer:

We have to use Newton Raphson method.

$ x_1=0.75 \ \Rightarrow f(x_1) \approx 2.2 , \ \ f'(x_1)= ? $

I can not find out what is $ f'(x_1) \ $ ?

Can anyone help me?

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Your really need to know the function f(x) to find its derivative. The slope of the graph at x = .75 appears to be > 0.