Suppose that you are asked to find the point on the curve y=ln(x) such that the tangent line passes through the point (3,5). The point on the curve cannot be found explicitly in closed form, but it can be approximated. First find an equation that you can solve that will give you the point you are looking for. Then use whatever algebraic method you want for approximating the solution (the bifurcation method is easy to use, but it is not very quick. Newton’s method is quick, if you remember how to use it) Can you generalize this problem?

Q: You are asked to find the equation of a horizontal tangent line to the curve y=3x3+2ex+2x. Use…

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Q: How do you find the equation of the tangent line to the parabola for y = x2 − 3x − 1 at x = 4.

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Q: Find the equation of the line tangent to the curve f(x) =x + at the point (5, 26/25)

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Q: Find the equation of the tangent line to the curve (a lemniscate) 2(x + y²) = 25(x² – y?) a the…

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Q: Find the equation(s) of the tangent line(s) to the graph of the curve y-x-12x through the point (1,…

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Q: The slope of the tangent line to the parabola y = 2x² + 7x + 7 at the point (4, 67) is: The equation…

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