Question #b399e Calculus Applications of Derivatives Using Newton's Method to Approximate Solutions to Equations 1 Answer Wataru Apr 1, 2017 #x_3 approx 1.5215# Explanation: You are on the right track! Let #f(x)=2x^(-1)-x^2+1 Rightarrow f'(x)=-2x^(-2)-2x# #x_1=2# #x_2=x_1-f(x_1)/(f'(x_1))=2-f(2)/(f'(2))=14/9# #x_3=x_2-f(x_2)/(f'(x_2))=14/9-f(14/9)/(f'(14/9)) approx 1.5215# Answer link Related questions How do you use Newton's Method to approximate #root5(20) # ? How do you use Newton's Method to approximate the value of cube root? How do you use Newton's Method to approximate the root of the equation #x^4-2x^3+5x^2-6=0# on... How do you use Newton's Method to approximate the positive root of the equation #sin(x)=x^2# ? If a rough approximation for ln(5) is 1.609 how do you use this approximation and differentials... How do you use linear approximation to estimate #g(2.95)# and #g(3.05)# if you know that #g(3)=-5#? How do you use a linear approximation to estimate #g(0.9)# and #g(1.1)# if we know that #g(1)=3#... How do you use differentials to estimate the value of #cos(63)#? When do you use newton's method? What is the local linearization of #e^sin(x)# near x=1? See all questions in Using Newton's Method to Approximate Solutions to Equations Impact of this question 2064 views around the world You can reuse this answer Creative Commons License