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Marcus Tool and Die Company produces a specialized milling tool designed specifically for machining ceramic components. Each milling tool sells for $4, so the company's revenue in dollars for x units sold is R(x) = 4x. The company's cost in dollars to produce x tools can be modeled as C(x) = 304+30x^(5/8). Use Newton's method to find the break-even point for the company (that is, find x such that C(x) = R(x)). Use x = 370 as your initial guess and show all your work. Thank you!
If this turns out to be an elaborate multi-step problem, please let me know so that I can compensate you for your time via PayPal. Again, I appreciate the help.
Set up the equation describing the problem
let f(x) be
the derivative of this is
When your first guess (x_{1}) is 370 the second estimate (x_{2}) will be
When you have a second estimate repeat the procedure but replace 390 with your second estimate.