Calculus

posted by .

Use analytical methods to find the exact global maximum and minimum values of the function f(x)=8x-ln(4x) for x >0. If a global maximum or minimum does not exist, enter the word NONE.

For the global maximum at x=none, But for the Global minimum at x=?

Is the Global minimum 0 or nonw? Any help would be greatly appreciated.

  • Calculus -

    I always encouraged my students to make a rough sketch of the graph.
    Pick any 5 or 6 positive x's, then find their y values.
    Pick an x close to zero (e.g. x = .00001) and see what y you get. This gives you an indication of the graph does close to zero. (remember x cannot be zero for this function)

    In general, the max/min is found by setting the derivative equal to zero, solving for the variable, and then subbing that back into the original equation.
    so
    f(x) = 8x - ln(4x)
    f'(x) = 8 - 1/x
    set this equal to zero, you will get x = 1/8

    I will let you find the minimum.

  • Calculus -

    y = 8 x - ln (4x)
    y' = 8 -4/x
    when is that zero?
    4/x = 8
    x = 1/2
    is that a maximum or a minimum?
    y" = 0 +4/x^2
    for x>0, y" is positive so it is a minimum
    so minimum at x = 1/2
    what is the value of the function at that minimum?
    y = 8(1/2) - ln 2
    4 - ln 2 = about 3.3

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    Find the points at which y = f(x) = 5x−ln(5x) has a global maximum, a global minimum, and a local, non-global maximum on the interval .1 ≤ x ≤ 2. Round your answers to two decimal places. Global Minimum: (x,y) = (,) …
  2. calculus

    Find the points at which y = f(x) = x8−13x has a global maximum and minimum on the interval 0 ≤ x ≤ 3.7. Round your answers to two decimal places. Global Maximum: (x,y) = (,) Global Minimum: (x,y) = (,)
  3. Math: Calculus

    Answer the following questions for the function f(x)=sin(x/4)^2 defined on the interval [-12.266371, 2.241593]. Rememer that you can enter pi for as part of your answer. a.)f(x) is concave down on the interval ____. b.) A global minimum …
  4. Calculus

    f(x) = sin^2(x/2) defined on the interval [ -5.683185, 1.270796]. Remember that you can enter pi for \pi as part of your answer. a.) f(x) is concave down on the interval . b.) A global minimum for this function occurs at . c.) A local …
  5. Calculus

    Answer the following questions for the function f(x) = sin^2(x/3) defined on the interval [ -9.424778, 2.356194]. Rememer that you can enter pi for \pi as part of your answer. a.) f(x) is concave down on the interval . b.) A global …
  6. math

    Answer the following questions for the function f(x)=sin^2(x/5) defined on the interval .(-15.507923,3.82699075) Rememer that you can enter "pi" for as part of your answer. a.what is f(x) concave down on the region B. A global minimum …
  7. Calculus

    Find the points at which y = f(x) = x^11-6x has a global maximum and minimum on the interval 0 ¡ x ¡ 4 Round your answers to two decimal places. Global Maximum: (x,y) = (,) Global Minimum: (x,y) = (,)
  8. Calculus

    Find the points at which y = f(x) = x^11-6x has a global maximum and minimum on the interval 0 ¢®A x ¢®A 4 Round your answers to two decimal places. Global Maximum: (x,y) = (,) Global Minimum: (x,y) = (,)
  9. Caluclus

    Find the absolute maximum and absolute minimum of f on the interval (-1,2]: f(x)=(-x^3+x^2+3x+1)/(x+1) A. Maximum: (1, -2); Minimum: (-1, 2) B. Maximum: (1, -2); Minimum: None C. Maximum: None; Minimum: None D. Maximum: None; Minimum: …
  10. math

    Find the value(s) of x for the following. (Enter your answers as a comma-separated list.) f(x) = 6 sin^2 x − 6 cos x, and the interval is 0 is less than or equal to x and x is less than or equal to pi. (a) f(x) has a local maximum …

More Similar Questions