calculus
posted by Yoona .
3. Given the function defined by y = x + sinx for all x such that π/2<=x<=3π/2
a. Find the coordinate of all maximum and minimum points on the given interval. Justify your answers.
b. Find the coordinates of all points of inflection on the given interval. Justify your answers.
please be explisive!
thanks!

calculus 
Damon
dy/dx = 1 + cos x
0 when cos x = 1
that is when x = pi
d^2y/dx^2 = sin x
sin x = 0 when x = pi
so this is not a max or min but a point of inflection 
calculus 
Damon
now look at the ends
at x =  pi/2
y =  pi/2 + sin(pi/2) = pi/2 1
minimum I bet
at x = 3 pi/2
y = 3 pi/2 + sin (3 pi/2) = 3 pi/2 1
maximum
Respond to this Question
Similar Questions

Calculus  Functions?
#1. A cubic polynomial function f is defined by f(x) = 4x^3 +ax^2 + bx + k where a, b and k are constants. The function f has a local minimum at x = 1, and the graph of f has a point of inflection at x= 2 a.) Find the values of a … 
calculus
4. Given the function f defined by f(x) = cos2x for π≤ x ≤π a. Find the xintercepts of the graph of f. b. Find the x and y coordinates of all relative maximum points of f. Justify your answer. c. Find the intervals … 
calculus
Find the absolute maximum and absolute minimum values of f on the given interval [π/4, 7π/4]. (Round all answers to two decimal places.) f(t) = t + cot(t/2) 
math
Question Part Points Submissions Used Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as … 
Calculus
The function f(x) is defined as f(x) = 2(x+2)(x1)^2 = 2(x^3 3x + 2) on the open interval (3,3). 1. Determine the xcoordinate of the absolute minimum of f(x) in the open interval (3,3). Justify your answer. 2. Find all values … 
Math, please help
Which of the following are trigonometric identities? 
AP CALC. AB
Let h be a function defined for all x≠0 such that h(4)=3 and the derivative h is given by h'(x)=(x^22)/(x) for all x≠0 a). Find all values of x for which the graph of h has a horizontal tangent, and determine whether … 
PreCal
An equation is given. (Enter your answers as a commaseparated list. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.) 2 cos 2θ − 1 = 0 a). Find all solutions of the equations … 
PreCal:(Cont.)
[Note: I've tried this problem 4 times already and still have it wrong. I know the steps to doing it but for some reason its wrong. an someone please help me get these answers for (b).] An equation is given. (Enter your answers as … 
Need Help Please PreCalc
The coordinates of the five quarter points for y=sin(x) are given below. Use these quarter points to determine the ycoordinates of the quarter points of y=5sin(π/3x). (0,0) (π/2,1) (π,0) (3π/2,1) (2π,0) …