Results 1 to 4 of 4

Math Help - second derivative/point of inflection

  1. #1
    Junior Member
    Joined
    Oct 2008
    Posts
    34

    Red face second derivative/point of inflection

    Given f(x) = e^(-5x) sin(1x) , 0< x < pi/2

    a) Find the second derivative

    b) suppose that f has a point of inflection at x=c. Using the result of a), you can formulate the equation for c in the form:
    tan 1c = K
    where K is some constant.
    Find the constant K as well as the points of inflection

    C) Find the (open) intervals of concavity. If there is more than one interval enter using the union symbol U. Enter the empty set as {}
    "f is concave upward on open intervals _________"
    "f is concave downward on open intervals _________"

    Alright so i found the second derivative:
    f''(x) = e^(-5x) * (24sinx - 10cosx)

    and in order for there to be inflection points where x = c, f''(c) = 0
    I also know that for finding concavity(part c) i need to test points, which i can do on my own once i figure out part b!
    I'm stuck on isolating "c" , i know this seems like grade 2 stuff by now, but still.
    here's where i'm at ..

    0 = e^(-5x) * (24sinx - 10cosx)
    0 = ln[e^(-5x)] * (24sinx - 10cosx)
    0 = (-5x) ln(e) * (24sinx - 10cosx)

    we replace x with c..
    0 = (-5c) ln(e) * (24sinc- 10cosc)

    but i get so lost here. How do i isolate??! obviously i'm missing something/have done something wrong.


    thanks for your help
    Britt
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by williamb View Post
    Given f(x) = e^(-5x) sin(1x) , 0< x < pi/2

    a) Find the second derivative

    b) suppose that f has a point of inflection at x=c. Using the result of a), you can formulate the equation for c in the form:
    tan 1c = K
    where K is some constant.
    Find the constant K as well as the points of inflection

    C) Find the (open) intervals of concavity. If there is more than one interval enter using the union symbol U. Enter the empty set as {}
    "f is concave upward on open intervals _________"
    "f is concave downward on open intervals _________"

    Alright so i found the second derivative:
    f''(x) = e^(-5x) * (24sinx - 10cosx)

    and in order for there to be inflection points where x = c, f''(c) = 0
    I also know that for finding concavity(part c) i need to test points, which i can do on my own once i figure out part b!
    I'm stuck on isolating "c" , i know this seems like grade 2 stuff by now, but still.
    here's where i'm at ..

    0 = e^(-5x) * (24sinx - 10cosx)
    0 = ln[e^(-5x)] * (24sinx - 10cosx)
    0 = (-5x) ln(e) * (24sinx - 10cosx)

    we replace x with c..
    0 = (-5c) ln(e) * (24sinc- 10cosc)

    but i get so lost here. How do i isolate??! obviously i'm missing something/have done something wrong.


    thanks for your help
    Britt
    Okay, so your second derivative is correct, and you want to know when it is eqaul to zero so...

    0=e^{-5x}[24\sin(x)-10\cos(x)]

    so from here use the zero factor rule

    so we get

    e^{-5x}=0 or 24\sin(x)-10\cos(x)=0

    Since e never equals zero the first has no solutions but

    24\sin(x)-10\cos(x)=0 \iff 24\sin(x)=10\cos(x) \iff
     \tan(x)=\frac{10}{24} \iff x=\tan^{-1}\left( \frac{5}{12}\right)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2008
    Posts
    34
    AH BUT OF COURSE!
    It's been a long day,
    you're greatly appreciated thankyou!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Oct 2008
    Posts
    34
    AH dang i spoke too soon
    So to find concavity, i need to find the first and second derivatives and equate to zero in order to find the critical and inflection points right?

    well if f'(x) = e^-5x (-5sinx + cosx)
    then if we set to zero, how do we find these points?
    (-5sinx + cosx) = 0
    sinx = 0 at pi, cosx = 0 at pi/2 and 3pi/2
    do i just use number values of those?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Point of Inflection (second derivative)- easy
    Posted in the Calculus Forum
    Replies: 4
    Last Post: June 6th 2010, 05:14 PM
  2. point of inflection
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 24th 2009, 05:27 PM
  3. Replies: 1
    Last Post: November 21st 2009, 06:42 PM
  4. Replies: 0
    Last Post: November 3rd 2009, 10:18 AM
  5. Replies: 2
    Last Post: July 23rd 2007, 09:38 PM

Search Tags


/mathhelpforum @mathhelpforum