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 6864 views around the world You can reuse this answer Creative Commons License