How do you find the linearization at a=81 of #f(x) = x^(3"/"4)#? Calculus Applications of Derivatives Using the Tangent Line to Approximate Function Values 1 Answer Jim H · mason m Aug 21, 2017 #L = f(a)+f'(a)(x-a)# (This is an equation of the tangent line at #(a,f(a))#) Explanation: #f(x) = x^(3/4)#, #a = 81# #f(81) = (root(4)81)^3 = 3^3 = 27# #f'(x) = 3/(4x^(1/4))#, so #f'(81) = 3/(4root(4)81) = 3/4*1/4# #L = 27+1/4(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 5587 views around the world You can reuse this answer Creative Commons License
