How do you use the first and second derivatives to sketch # y=(x+2)/(x-1)#? Calculus Graphing with the Second Derivative Examples of Curve Sketching 1 Answer Harish Chandra Rajpoot Jun 24, 2018 #y'=-3/(x-1)^2#, #y''=6\(x-1)^3# Explanation: Given: #y=\frac{x+2}{x-1}# #\frac{dy}{dx}=\frac{(x-1)\frac{d}{dx}(x+2)-(x+2)\frac{d}{dx}(x-1)}{(x-1)^2}# #\frac{dy}{dx}=\frac{(x-1)\cdot1-(x+2)\cdot1}{(x-1)^2}# #\frac{dy}{dx}=\frac{-3}{(x-1)^2}# #\frac{d^2y}{dx^2}=-3\frac{d}{dx}\frac{1}{(x-1)^2}# #\frac{d^2y}{dx^2}=-3\cdot\frac{-2}{(x-1)^3}# #\frac{d^2y}{dx^2}=\frac{6}{(x-1)^3}# Answer link Related questions How do you sketch the curve #f(x)=x+sqrt(1-x)# ? How do you sketch the curve #f(x)=e^x/(1+e^x)# ? How do you sketch the graph of #f(θ)=2cosθ+cos2 θ# for #0≤x≤ 2π# using the first and second derivative? How do you graph #y = 2x^3 - 4x + 1# using the first and second derivative? How do you graph #F(x,y)=sqrt(x^2+y^2-1)+ln(4-x^2-y^2)#? How do you sketch #f(x,y)=arcsin(x^2+y^2-2)#? How do you graph #f(x,y) = 10 - 4x - 4y#? How do you graph of the function #y=arctan(x)#? How do you sketch the graph of #f(x)=x^3-3x^2#? How do you graph #f(x) = xsqrt(4-x^2)# See all questions in Examples of Curve Sketching Impact of this question 1570 views around the world You can reuse this answer Creative Commons License