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 1720 views around the world You can reuse this answer Creative Commons License