October 15th, 2007, 08:10 AM  #1 
Newbie Joined: Oct 2007 From: waterloo Posts: 2 Thanks: 0  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). 
October 15th, 2007, 10:38 AM  #2 
Senior Member Joined: Sep 2007 From: USA Posts: 349 Thanks: 67 Math Focus: Calculus 
A way to solve this is by using derivatives. The equation of a tangent line to a function f(x) is y=f '(x0)(xx0)+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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