Consider the autonomous DE dy/dx = y² - y - 6.Use your ideas from Problem 35 to ­find intervals on the y-axis for which solution curves are concave up and intervals for which solution curves are concave down. Discuss why each solution curve of an initial-value problem of the form dy/dx = y² - y - 6, y(0) = y₀, where -2 < y₀ < 3, has a point of inflection with the same y coordinate. What is that y-coordinate? Carefully sketch the solution curve for which y(0) = -1. Repeat for y(2) = 2.

Data from problem 35

Using the autonomous equation (2), discuss how it is possible to obtain information about the location of points of inflection of a solution curve.