How do you find the linear approximation of a function? Calculus Applications of Derivatives Using the Tangent Line to Approximate Function Values 1 Answer Wataru Sep 21, 2014 The linear approximation #L(x)# of a function is done using the tangent line to the graph of the function. The equation of the tangent line at #x=a# is given by #y=f'(a)(x-a)+f(a)#, the linear approximation is #L(x)=f'(a)(x-a)+f(a)#. Answer link Related questions How do you find the linear approximation of #(1.999)^4# ? 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)# ? What is the linear approximation of a function? See all questions in Using the Tangent Line to Approximate Function Values Impact of this question 7524 views around the world You can reuse this answer Creative Commons License