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 ยท 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 5739 views around the world You can reuse this answer Creative Commons License
