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Homework Help: calculus

Posted by Yoona on Sunday, December 18, 2011 at 11:24pm.

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, Monday, December 19, 2011 at 1:53am

  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, Monday, December 19, 2011 at 1:58am

  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
  

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