Question #54db1 Calculus Applications of Derivatives Using the Tangent Line to Approximate Function Values 1 Answer Jim H Feb 23, 2017 #L(x) = f(a) + f'(a)(x-a)# Explanation: In this case #f'(x) = 2/3x^(-1/3)# so #f'(a) = f'(27) = 2/9#. And #f(a) = f(27) = 9# #L(x) = 9 + 2/9(x-27)# # = 9+.22bar(2)(x-27)# 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 6694 views around the world You can reuse this answer Creative Commons License