# calculus

posted by .

Find all relative extrema and points of inflection of the function:

f(x) = sin (x/2)

0 =< x =< 4pi

=< is supposed to be less than or equal to.

I can find the extrema, but the points of inflection has me stumped. The inflection point is (2pi,0) but shouldn't there be inflection points on x=0 and x=4pi as well?

• calculus -

The basic sine curve has points of inflection at every x-intercept of the curve,

y' = (1/2) cos x/2
y' = -(1/4) sin x/2

-(1/4)sin x/2 = 0
gives me x/2 = 0 or x/2 = π or x/2 = 2π etc
or
x = 0 or x = 2π or x = 4π etc

then if you domain is 0 ≤ x ≤ 4π
you are correct, there should have been points of inflection at
(0,0), (2π,0) and (4π,0)

## Similar Questions

1. ### calculus

find the relative extrema and points of inflection, if possible, of y = xln((x^4)/8) Any help would be awesome...thanks! (i know that the relative extrema come from critical values from y' and points of inflection come from y'')
2. ### math

Given the function f(x)=x^4−6x^2 a.) Find all values of x where local extrema points occur b.)find all values of x where inflection points occur c.) find all local extrema of f(x) d.) find all global extrema of f(x) over the …
3. ### calculus

Find any relative extrema and any points of inflection if they exist of f(x)=x^2+ ln x^2 showing calculus. Please show work in detail so I can follow. Thanks. The answer is no relative max or min and the points of inflection are (1,1) …
4. ### Calculus A

Find all relative extrema and points of inflection for the following function... h(X)= X^2+5X+4/ X-1 min= max= inflection points=
5. ### Calculus A

Find all relative extrema and points of inflection for the function; h(x)=(x^2+5x+4)/(x-1)
6. ### Math

Find x-value of all points where function has relative extrema and find the Values of these extrema. f(x)= (x^2)/(ln(x))
7. ### Calculus

Find the x-values of all points where the function below has any relative extrema. Find the values(s)of any relative extrema. G(x)=(x-3)^2/x-4. How do I solve this?
8. ### Relative Extrema: AP Calculus

Consider the function f(x)= (3/4)x^4-x^3-3x^2+6x Find the relative extrema for f(x); be sure to label each as a maximum or minimum. You do not need to find function values; just find the x-values. Determine the interval(s) where f(x) …
9. ### Calculus AB

Find the x-coordinates of any relative extrema and inflection point(s) for the function f(x) = 3x(1/3) + 6x(4/3). You must justify your answer using an analysis of f '(x) and f "(x). My start to a solution: x-values: (-1/8) and (-1/4) …
10. ### Calculus

Find the x-coordinates of any relative extrema and inflection point(s) for the function f(x)=9x^1/3+9/2x^4/3. I've gotten -0.5 as the relative minimum and x=1 for the inflection points. Is this correct?

More Similar Questions