1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Horizontal Tangent Line

  1. Apr 21, 2008 #1
    1. The problem statement, all variables and given/known data

    Find all points on the graph of the function at which the tangent line is horizontal.

    f(x) = 2sinx + (sinx)^2

    2. Relevant equations
    Hi guys I have an issue. I do not know how to approach this problem.

    I know the chain rule but I still do not know how to solve the prolem.

    Thank you for your help.

    3. The attempt at a solution
     
  2. jcsd
  3. Apr 21, 2008 #2
    the tangent line is the slope of f(x) at some point, how do you find that slope?
     
  4. Apr 21, 2008 #3
    The derivative of the function gives you the slope of the tangent line at each point x.

    How do you know when a line is horizontal?

    Now, how can you find which points have horizontal lines?
     
    Last edited: Apr 21, 2008
  5. Apr 21, 2008 #4

    exk

    User Avatar

    what is the slope of a horizontal line?
     
  6. Apr 21, 2008 #5
    slope is always rise over run; if its instantaneous then its derivative of rise of derivative of run.
    if its an entire straight line, the slope is rise over run. So, whats the rise per unit of run?
     
  7. Apr 22, 2008 #6

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    nejnadusho, the ball is back in your court! Everyone is asking you the same question: what is the slope of a horizontal line?
     
  8. Apr 22, 2008 #7
    Ok
    I am sorry there was something wrong and I could not open the page yestarday.
    I guess I should find the derivative of the f(x) which means I should find f'(x) and after
    the equation of the tangent line . right?

    And i guess the slope is horizontal when the f(x) of the slope equals ohhh no.
    When x of the function of the slpope is 0(zero) right?
     
  9. Apr 22, 2008 #8

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    I hope that means 'when f'(x)=0'.
     
  10. Apr 22, 2008 #9
    Actually
    I got lost again because I found the derivative
    but How am I suppose to find the equation of the tangent line when I do not have a certain point.

    Do I need it actually?
    I mean some point?

    So if I substitute x by 0 I am gonna find the point where the slope of the tangent line is 0 ????
     
    Last edited: Apr 22, 2008
  11. Apr 22, 2008 #10

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    It doesn't ask you for the equation of the tangent line. It's asks you for what values of x and y does the tangent line have zero slope. Start by finding the x values.
     
  12. Apr 22, 2008 #11

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Tell us what you got for f'(x). Write the equation f'(x)=0. Now try to solve for x.
     
  13. Apr 22, 2008 #12
    So if I substitute x by 0 I am gonna find the point where the slope of the tangent line is 0 ????

    But I am going to find only one y for each x so how am I suppose to find more than one zero slope if there is?
     
  14. Apr 22, 2008 #13

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    If you 'substitute x by 0' you are gonna find the slope of the tangent line at x=0. You want to know where the slope is zero. Tell us what you got for f'(x). Write the equation f'(x)=0. Now try to solve for x.
     
  15. Apr 22, 2008 #14
    ok
    f'(x)= 2cos x (sin x + 1)
    2cos x (sin x + 1) = 0
     
  16. Apr 22, 2008 #15
    ok but how am I suppose to solve it for x now?
     
  17. Apr 22, 2008 #16

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Good! You've even factored it. If the product of those factors is 0, then either cos(x)=0 OR (sin(x)+1)=0. For what values of x is cos(x)=0?
     
  18. Apr 22, 2008 #17
    Pi/2 for cosx

    and ((3*Pi)/2) for sin
     
  19. Apr 22, 2008 #18
    I am dum

    I stay I am doing something and I cannot realize that I just solve the problem.
     
  20. Apr 22, 2008 #19

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Good so far, but the problems asks for ALL points. E.g. cos(3pi/2)=0, cos(5pi/2)=0, etc. etc. And sin(-pi/2)=(-1) and sin(7pi/2)=(-1). Can you clearly describe all of them? Once you've done that, you just need to get the corresponding y values.
     
  21. Apr 22, 2008 #20
    Thank you very much for the way you helped me.
    Thank you very much guys.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?