Results 1 to 6 of 6

Math Help - Concavity and the Derivative of e^x

  1. #1
    Member
    Joined
    Sep 2009
    From
    Ontario
    Posts
    162

    Concavity and the Derivative of e^x

    Let f be the function given by f(x)=2xe^(x). The graph of f is concave down when A)x<-2 B)x>-2 C)x<-1 D)x>-1 E)x<0

    I know that you can use the 2nd derivative to find concavity. If f''(x) is negative, it is concave down and if its f''(x) is positive, its concave up

    However, i don't know how to find f''(x) of this function
    Please Help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    Quote Originally Posted by rawkstar View Post
    Let f be the function given by f(x)=2xe^(x). The graph of f is concave down when A)x<-2 B)x>-2 C)x<-1 D)x>-1 E)x<0

    I know that you can use the 2nd derivative to find concavity. If f''(x) is negative, it is concave down and if its f''(x) is positive, its concave up

    However, i don't know how to find f''(x) of this function
    Please Help
    f(x) = 2x \cdot e^x

    product rule ...

    f'(x) = 2x \cdot e^x + 2e^x

    f'(x) = 2e^x(x + 1)

    do the product rule again ...
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Sep 2009
    From
    Ontario
    Posts
    162
    i'm guessing the the derivative of 2e^x is still 2e^x

    is it

    f''(x)=(2e^x)[1+(x+1)]
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    Quote Originally Posted by rawkstar View Post
    i'm guessing the the derivative of 2e^x is still 2e^x

    is it

    f''(x)=(2e^x)[1+(x+1)]
    simplify ...

    f''(x) = 2e^x(x+2)

    now finish the problem
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Sep 2009
    From
    Ontario
    Posts
    162
    ok so
    0=(2e^x)(x+2)
    I distributed to get
    0=2xe^x+4e^x
    and i don't know how to solve from here (i'm not quite sure how to use natural log)
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    f''(x) = 2e^x(x+2) = 0

    x = -2
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: November 15th 2010, 02:08 AM
  2. Concavity
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 11th 2009, 06:40 AM
  3. Concavity and Second Derivative
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 21st 2009, 02:41 PM
  4. Concavity and Second Derivative
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 21st 2009, 01:12 PM
  5. concavity...why?
    Posted in the Calculus Forum
    Replies: 8
    Last Post: November 7th 2008, 03:01 PM

Search Tags


/mathhelpforum @mathhelpforum