What is the equation of the line tangent to #f(x)=1/abs(x) # at #x=1#? Calculus Derivatives Tangent Line to a Curve 1 Answer Eddie Aug 24, 2016 #y = -x + 2# Explanation: at #x = 1, abs x = x# so #f(x) = 1/x# #f(1) = 1# # f'(x) = - 1/x^2# # f'(1) = -1 # #y - y_0 = m (x - x_o)# #implies y - 1 = -1(x - 1)# #y = -x + 2# 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 1044 views around the world You can reuse this answer Creative Commons License