October 15th, 2007, 09:10 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, 11:38 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 

Tags 
line, problem, tangent 
Search tags for this page 
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Tangent Line Problem  Shamieh  Calculus  6  September 25th, 2013 06:05 PM 
Secant line becoming a tangent line  Lucida  Trigonometry  2  May 19th, 2012 02:01 AM 
Tangent line  johnny  Calculus  5  June 25th, 2011 04:25 PM 
Tangent line  johnny  Calculus  3  March 31st, 2011 09:44 PM 
A problem concerning a tangent line and a circle  Lax  Trigonometry  5  September 10th, 2008 04:28 PM 