1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Differentiation Question

  1. Jan 15, 2010 #1
    1. The problem statement, all variables and given/known data
    Find a function of the form [tex] f(x) = a + b \cos cx [/tex] that is tangent to the line [tex]y = 1[/tex] at the point [tex](0,1)[/tex], and tangent to the line [tex]y = x + 3/2 - \pi /4[/tex] at the point [tex](\pi /4 , 3/2)[/tex].

    2. Relevant equations

    3. The attempt at a solution
    [tex]f(0) = a + b = 1[/tex], so [tex]a = 1 - b[/tex].

    This is as far as I can get though.

    [tex]f'(0) = -bc \sin cx = 0[/tex]

    for any a, b, and c, and

    [tex]f(\pi /4) = (1 - b) + b \cos [(\pi /4)c] = 3/2[/tex]


    [tex]f'(\pi /4) = -bc \sin [(\pi /4)c] = 1[/tex]

    don't really seem to help me.

    What am I missing?
  2. jcsd
  3. Jan 16, 2010 #2
    Well you can combine the last two equations to get
    [tex]b\left[\cos\left(\frac{c\pi}{4}\right)-c\sin\left(\frac{c\pi}{4}\right)-1\right] = \frac{3}{2}.[/tex]
    Presumably this will give you infinitely many solutions. For instance, c = 2 works.
  4. Jan 16, 2010 #3
    the function has a maximum at x = 0, because ymax = a+b
    if you do the second derivative test you will find -bc^2 < 0
    so b>0

    i am not able to tell more than this from the given data
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook