How do you find the linearization at x=2 of #f(x) = 3x - 2/x^2#? Calculus Applications of Derivatives Using the Tangent Line to Approximate Function Values 1 Answer VinÃcius Ferraz Jun 11, 2017 Taylor: #11/2 + 13/4(x - 2) + O(x-2)^2# Explanation: #f'(x) = 3 + 2/x^3 => f'(2) = 3 + 2/8 = 13/4# #L(x) = 13/4x + b and L(2) = f(2)# #f(2) = 6 - 2/4 = 11/2# #13/4 * 2 + b = 11/2 => b = 1# The tangent line at x = 2 is #L(x) = 13/4 x + 1# Answer link Related questions How do you find the linear approximation of #(1.999)^4# ? How do you find the linear approximation of a function? How do you find the linear approximation of #f(x)=ln(x)# at #x=1# ? How do you find the tangent line approximation for #f(x)=sqrt(1+x)# near #x=0# ? How do you find the tangent line approximation to #f(x)=1/x# near #x=1# ? How do you find the tangent line approximation to #f(x)=cos(x)# at #x=pi/4# ? How do you find the tangent line approximation to #f(x)=e^x# near #x=0# ? How do you use the tangent line approximation to approximate the value of #ln(1003)# ? How do you use the tangent line approximation to approximate the value of #ln(1.006)# ? How do you use the tangent line approximation to approximate the value of #ln(1004)# ? See all questions in Using the Tangent Line to Approximate Function Values Impact of this question 3342 views around the world You can reuse this answer Creative Commons License