You are given the equation of the line y=x^3+x^2-2x. Find the stationary points of the curve and determine the maximum and minimum points and find where it crosses the x-axis and thus sketch the graph

First differentiate the equation to find the equation of the tangents in terms of x. From this set dy/dx=0 because this is the stationary points, from this use the quadratic equation to find the value of x for the stationary points. Next differentiate again and substitute the values for the stationary points to determine the maximum and minimum points. The minimum and maximum points are determined by when dy/dx is greater than or less than 0To find the points when it crosses the x-axis substitute out x producing a quadratic which can be factorised which produces x=0, x=1,x=-2. From all these you can sketch the graph of y