# 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.

## 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