Graded Paths Lesson

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These are two surfaces used in a lesson published by Margaret Reese (citation below). The lesson gives students the formulas for the surfaces of two "mountains": f(x,y) = 100 - 2x2 - y2 g(x,y) = 100 + 3x2 - 2y2 Students are then asked to use the use the tools of mutlivariable calculus and differential equations to find (for a given starting point): The steepest possible path up the mountain A path which ascends the mountain at 50% of the maximum possible steepness. A path which ascends the mountain at a constant grade of 50%. When assigning this project, I had students sketch the paths they found on the model. Project source: Reese, Margaret. Computing Project for Multivariable Calculus. PRIMUS. Vol. 6, Iss. 2, 1996.