
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
August 30th, 2011, 06:38 PM  #1 
Joined: Aug 2011 From: United States Posts: 32 Thanks: 0  Find k such that the line is tangent to the function.
I am having extreme trouble with this differentiation problem. It says, "Find k such that the line is tangent to the graph of the function." Function F(x) = x^2  kx Line y = 4x  9 I don't understand the step where you set f(x) to equal y. How do you get rid of the k? 
August 30th, 2011, 08:30 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 6,688 Thanks: 529 Math Focus: Elementary mathematics and beyond  Re: Fine k such that the line is tangent to the function. so the slope of the line and the function are the same (one condition of tangency). so the line and curve intersect (other condition of tangency). so k = 2, 10. 
August 31st, 2011, 04:16 AM  #3 
Senior Member Joined: Sep 2007 Posts: 2,409 Thanks: 5  Re: Fine k such that the line is tangent to the function.
Fermat, prior to Newton and Leibniz, had a method for problems like this. It uses the fact that a tangent line has a "second order" intersection with a curve. That is, if f(x) is tangent to t(x) at , must be a double root of f(x)= g(x). Your given curve is and your desired tangent line is so we look at the equation which is the same as . By the quadratic formula, solutions are given by . There will be a double root if and only if the discriminant, . Solve that equation for two values of k. 

Tags 
find, function, line, tangent 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Find the equation of the tangent line to G(x) .  Shamieh  Calculus  2  October 7th, 2013 05:12 AM 
Find the equation of the tangent line (3)  Shamieh  Calculus  1  October 4th, 2013 11:48 PM 
Find the equation of the tangent line (2)  Shamieh  Calculus  2  October 4th, 2013 07:20 PM 
Find an equation of the Tangent Line  Shamieh  Calculus  3  September 23rd, 2013 02:16 PM 
Find Equation of tangent line  chelsea  Calculus  3  November 17th, 2012 06:40 PM 