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October 15th, 2007, 08:10 AM   #1
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A tangent line problem

Hello, could someone give me some ideas on this problem please? thanks

Find the equation of everyline which passes through point (3,4) and is tangent to curve y=2*sqrt(x).
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October 15th, 2007, 10:38 AM   #2
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A way to solve this is by using derivatives. The equation of a tangent line to a function f(x) is y=f '(x0)(x-x0)+f(x0), where x0 is the x value of where the line is tangent to f(x). In this case, we have y=x/sqrt(x0)+sqrt(x0). Substitute 3 for x and 4 for y and solve for x0.
4=3/sqrt(x0)+sqrt(x0). The solutions for x0 are 1 and 9. Therefore, the possible lines are:
y=x+1
y=x/3+3
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