What is the equation of the line tangent to #f(x)=(x^3 - 4) / x# at #x=2#? Calculus Derivatives Tangent Line to a Curve 1 Answer Bdub Mar 18, 2016 #y-2=5(x-2)# #y-2=5x-10# #y=5x-8# Explanation: #f(x)=x^3/x -4/x# #f(x)=x^2-4x^-1# #f'(x)=2x+4/x^2# #f'(2)=4+1=5# #f(2)=(2^3-4)/2 = 4/2 = 2# #y-2=5(x-2)# #y-2=5x-10# #y=5x-8# Answer link Related questions How do you find the equation of a tangent line to a curve? How do you find the slope of the tangent line to a curve at a point? How do you find the tangent line to the curve #y=x^3-9x# at the point where #x=1#? How do you know if a line is tangent to a curve? How do you show a line is a tangent to a curve? How do you find the Tangent line to a curve by implicit differentiation? What is the slope of a line tangent to the curve #3y^2-2x^2=1#? How does tangent slope relate to the slope of a line? What is the slope of a horizontal tangent line? How do you find the slope of a tangent line using secant lines? See all questions in Tangent Line to a Curve Impact of this question 996 views around the world You can reuse this answer Creative Commons License