Graded Paths Lesson

thingiverse

Students are presented with two surfaces from a lesson developed by Margaret Reese (source cited below). The lesson provides students with formulas for the surfaces of two "mountains":\nf(x,y) = 100 - 2x^2 - y^2\ng(x,y) = 100 + 3x^2 - 2y^2\nUsing tools from multivariable calculus and differential equations, students are tasked to find, for a given starting point:\nThe steepest possible route up the mountain\nA path that ascends the mountain at 50% of its maximum steepness\nA path that ascends the mountain at a constant grade of 50%\nWhen assigning this project, I had students sketch the paths they found on the model.\nProject source: Reese, Margaret. Computing Project for Multivariable Calculus. PRIMUS. Vol. 6, Iss. 2, 1996