Compputing using Newtons Method

Here we define a little function to calculate the newton approximation: newton(f,var,start,iterations):= block([fp:diff(f,var),p:start,numer:true], for i:1 thru iterations do p: sublis([var=p],(p-f/fp)), p);done; produces Above Here First

• Compute with 3 iterations starting at x=2, newton(x^3-27,x,2.1,3) returns Result
• and with 7 iterations newton(x^3-27,x,2.1,7) evaluates to Result