calc

posted by .

find the absolute maximum and minimum for f(x) = x+ sin(x) on the closed interval [0, 2pi]

  • calc -

    f' = 1 + cos(x)
    f'=0 when cos(x) = -1, or x=pi

    however,
    f''(x) = -sin(x) which is also 0 at x=pi.

    So, (pi,pi) is an inflection point, not a max or min.

    f(2pi) = 2pi

    so that is the absolute max on [0,2pi]

    Note that f'(x) >= 0 for all x, so there is no max or min, which require changing direction.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    Find the absolute maximum and absolute minimum values of f(x)=sinx + (ã3) cosx on the closed interval [0,ƒÎ/3]
  2. calc

    let f(x)= -x^2 +3x on the interval [1,3] . Find the absolute maximum and absolute minimum of f(x) on this interval
  3. calc

    Let g(s)=1/(s-2)on the interval (0,1). Find the absolute maximum and absolute minimum of g(s) on this interval
  4. Calculus (pleas help!!!)

    Find the absolute maximum and absolute minimum values of the function f(x)=(x−2)(x−5)^3+11 on each of the indicated intervals. Enter -1000 for any absolute extrema that does not exist. (A) Interval = [1,4] Absolute maximum …
  5. Calculus (pleas help!!!)

    Find the absolute maximum and absolute minimum values of the function f(x)=(x−2)(x−5)^3+11 on each of the indicated intervals. Enter -1000 for any absolute extrema that does not exist. (A) Interval = [1,4] Absolute maximum …
  6. Absolute Extrema

    Find the minimum and maximum values of the function f(x)= 2/3 sin pix on the interval [1,2] (domain). I got (1.5, -2/3) as the minimum and no maximum on the interval. Is it correct?
  7. Calculus

    Find the absolute maximum and absolute minimum values of the function f(x)=x^3+6x^2-63x+4 on each of the indicated variables. Enter DNE for does not exist. (A) Interval = [-8,0] Absolute maximum = Absolute minimum = (B) Interval = …
  8. calculus

    2) Let g(s)= t(4−t)^1/2 on the interval [0,2]. Find the absolute maximum and absolute minimum of g(t) on this interval. Enter DNE if the absolute maximum or minimum does not exist. The absolute max occurs at t= . The absolute …
  9. Calc

    find absolute max and min of f(x)=cosx+sin^2(x) on interval [0,2pi]. Give exact answers, not decimal approx. (Use closed interval method)
  10. 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: …

More Similar Questions