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 (x1) is 370 the second estimate (x2) will be
When you have a second estimate repeat the procedure but replace 390 with your second estimate.