What is the equation of the tangent line of #f(x) =(e^3x-3x)(e^x-x)# at #x=1#? Calculus Derivatives Tangent Line to a Curve 1 Answer Roy E. Dec 30, 2016 Did you really mean #e^3x# or should it have been #e^x#? If so, then the tangent line is #y=(e-3)/(e-1)# because #f(x)# has a local minimum at #(1,(e-3)/(e-1))#. 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 1706 views around the world You can reuse this answer Creative Commons License