Choose a differentiable two-variable function f to create two animations illustrating: i) The tangent line at any point of a curve on the graph of f; ii) All tangent lines to some point on the graph of f. Can you show a step by step solution, and also do both animations using Geogebra or any other tool that you like?
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This is a paraboloid, and it's easy to visualize and work with. Step 2: Find the gradient The gradient of a function gives us the direction of steepest ascent at any point. It's a vector that points in the direction where the function increases the most. For a Show more…
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