What is the equation of the tangent line of #f(x)=sqrt(1/(x^2-3x+2) # at #x=0#? Calculus Derivatives Tangent Line to a Curve 1 Answer VinÃcius Ferraz Jun 7, 2017 #y = 3 / 2^(5/2)x + 1/2^(1/2)# Explanation: #p(x) = x^2 - 3x + 2 => f = p^(-1/2)# #f'(x) = -1/2 p^(-3/2) (2x - 3)# #f'(0) = -1/2 2^(-3/2) (-3) = + 3 * 2^(-5/2) = a# The desired line is #g(x) = ax + b# #g(0) = f(0) = sqrt{1/2} = b# 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 1320 views around the world You can reuse this answer Creative Commons License