October 5th, 2017, 08:21 PM  #1 
Member Joined: Apr 2017 From: New York Posts: 52 Thanks: 4  horizontal tangent line
Hi guys, I was wondering how I can solve this question attached. Let me show what I did here but couldn't conclude. Thanks all. f(x) = 2cos(x) + cos²(x) f'(x) = 2sin(x)  2sin(x)cos(x) => f '(x) = 2sin(x)(1 + cos(x)) and then here sin(x) = 0 OR cos(x) = 1 sin(x) is 0 at pi, 3pi, 5pi, etc. cos(x) is 1 at 0, 2pi, 4pi, ... that is it and then how could I continue? Last edited by skipjack; October 6th, 2017 at 03:51 AM. 
October 5th, 2017, 09:00 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,723 Thanks: 985 Math Focus: Elementary mathematics and beyond 
Some errors. The second line of your work is missing a minus sign but you've got it right in your third line. Also, $$\sin(x) = 0 \implies x = k\pi, \, k \in \mathbb{Z}$$ and $$\cos(x) = 1 \implies x = (2k  1)\pi, \, k \in \mathbb{Z}$$ Can you think of what to do next? (Hint: there are two extremes so you need to find two values to substitute into f(x).) Last edited by greg1313; October 5th, 2017 at 09:11 PM. 
October 6th, 2017, 08:49 AM  #3 
Member Joined: Apr 2017 From: New York Posts: 52 Thanks: 4 
Thanks Greg, how about the y values where tangent is horizontal? I want to compare with my work. thanks you were very helpful 
October 6th, 2017, 09:22 AM  #4 
Member Joined: Apr 2017 From: New York Posts: 52 Thanks: 4 
Am I going to plug in x value into original function or into derivative.


Tags 
calculus, cos or sin, horizontal, line, tangent 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Horizontal tangent line  nealed1  Calculus  1  March 15th, 2016 05:46 AM 
Horizontal Tangent  Luckman1  Calculus  1  May 21st, 2014 01:13 PM 
Change of x & y axis in case of Horizontal Tangent  zak100  Trigonometry  3  December 18th, 2013 02:14 PM 
Find the horizontal tangent line to the polynomial...  soulrain  Calculus  2  June 25th, 2012 09:15 AM 
Horizontal stretching about the line x=4  rancid1998  Elementary Math  1  April 25th, 2010 07:49 AM 