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!

Find line tangent to curve which is parallel to other line

  1. Mar 31, 2017 #1
    1. The problem statement, all variables and given/known data
    Find the line tangent to the curve f(x)=0.5x2+3x-1 which is parallel to the line g(x)=x/2+0.5

    2. Relevant equations
    f'(x)=x+3

    3. The attempt at a solution
    I know it involves taking the derivative of f(x) and using it somehow, but I don't know where to go from there.
     
  2. jcsd
  3. Mar 31, 2017 #2

    Math_QED

    User Avatar
    Homework Helper

    You want to find the tangent line to the curve ##f(x)##, parallel to the line ##g(x)##. If the tangent line has to be parallel with ##g(x)##, what do you know about the slope of this line?
     
  4. Mar 31, 2017 #3
    Both lines will need to have the same slope, 1/2.
     
  5. Mar 31, 2017 #4

    Math_QED

    User Avatar
    Homework Helper

    Correct. Now, the derivative gives the slope of the tangent line in each point. Where is the slope ##1/2##?
    Can you find the equation of the tangent line then?
     
  6. Mar 31, 2017 #5
    The slope is 1/2 when f'(x)=1/2:
    1/2=x+3
    x=-5/2
     
  7. Mar 31, 2017 #6

    Math_QED

    User Avatar
    Homework Helper

    Minor mistake in your arithmetic.

    You have a slope and a point (if you fix the mistake). There is a unique line that fits those 2 conditions. Can you find the equation?
     
  8. Mar 31, 2017 #7
    Yes caught the mistake.

    So using -5/2 on f(x) gets f(-5/2)=-43/8, which means a point on the line is (-5/2, -43/8).
    If the line is of the form y=1/2*x+b, we substitute the point for x and y:
    -43/8=1/2*-5/2+b
    b=-33/8
    The line is: y=1/2*x-33/8
     
  9. Mar 31, 2017 #8

    Math_QED

    User Avatar
    Homework Helper

    That's correct! Well done!
     
  10. Apr 1, 2017 #9

    Mark44

    Staff: Mentor

    Thread moved. @bubblescript, please post problems that involve derivatives in the Calculus & Beyond section.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Find line tangent to curve which is parallel to other line
Loading...