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Math Help - Single variable optimization

  1. #1
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    Single variable optimization

    I also got problem with this one

    Consider the function ln(x) + x/4 where 1 <_ x <_ 10

    a) Find all stationary points for f(x)
    b) Find all local extreme points and calculate local extreme values (ln (10) = (almost equal) 2.303)
    c) Calculate the second derivative and determine if the function is concave or convex on its
    domain. If not, where is it convex and where is it concave?

    First i have to derivate

    Then i get 1/x - 4x^-2 = 0

    How do i go further now?

    Thanks for the help
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  2. #2
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    Quote Originally Posted by Lippi86 View Post
    I also got problem with this one

    Consider the function ln(x) + x/4 where 1 <_ x <_ 10

    a) Find all stationary points for f(x)
    b) Find all local extreme points and calculate local extreme values (ln (10) = (almost equal) 2.303)
    c) Calculate the second derivative and determine if the function is concave or convex on its
    domain. If not, where is it convex and where is it concave?

    First i have to derivate

    Then i get 1/x - 4x^-2 = 0 Mr F says: The second term coresponds to the derivative of 4/x, whereas the function you posted says x/4 ... So which is it meant to be?

    How do i go further now?

    Thanks for the help
    If you're studying calculus you're expected to be proficient in pre-calculus. There are many ways of solving 1/x - 4x^-2 = 0. One way would be to start by multiplying both sides by x^2.
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