Calculus

Find the interval(s) where the function is increasing where and it is decreasing.
f(x)=sin(x+(pi/2)) for 0≤x≤2pi

so my derivative is f'(x)=cos(x+(pi/2))?
and my critical number is -pi/2?

  1. 👍 0
  2. 👎 0
  3. 👁 181
asked by sh
  1. cosine is positive for x +pi/2 = 0 to pi/2 and from 3 pi/2 to 2 pi

    when x+pi/2 = 0 then x = -pi/2 or 3pi/2
    when x + pi/2 = pi/2, x = 0
    so one interval is x = 3pi/2 to 0

    when x+pi/2 = 3 pi/2 then x = pi
    when x+pi/2 = 2 pi then x = 3 pi/2

    so second interval is frm x = pi to 3 pi/2

    so finally the entire interval from x = pi to x = 2 pi (which is 0) has a positive derivative, function increasing

    1. 👍 0
    2. 👎 0
    posted by Damon
  2. Wow, so confusing. Thanks!

    1. 👍 0
    2. 👎 0
    posted by sh
  3. So the whole interval is increasing? The function of cosx has a section of decreasing though.

    1. 👍 0
    2. 👎 0
    posted by sh

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    Given f(x)=sin(x)-2cos(x) on the interval [0,2pi]. Determine where the function is concave up and concave down, and increasing and decreasing. I have found that the answer for decreasing is (2.68,5.82). All answers are to be in

    asked by Shane on June 22, 2010
  2. calculus

    Given f(x)=sin(x)-2cos(x) on the interval [0,2pi]. a) Determine where the function is increasing and decreasing. b) Determine where the function is concave up and concave down. ________________________________________ I know:

    asked by Shawn on November 1, 2011
  3. Algebra

    Im having a hard time figuring out this problem: Use the function, y=-(x+1)^2 +2, to answer the following parts. The increasing interval and decreasing interval To find both I believe that: increasing : x < -1 decreasing : x > 1

    asked by Mike on May 5, 2011
  4. Please check my Calculus

    1. Given f(x)=-6/x, choose the correct statement A. The graph of f is concave upward on the interval (negative infinity, 0) B. The graph of f is concave downward on the interval (negative infinity, 0) C. The graph of f is concave

    asked by Anonymous on January 12, 2015
  5. increasing decreasing calc

    f(x)=x^3=12x-24 f'(x)=3x^2+12=0 3x^2=-12 x^2=-4 what is x. would it be x=-2 and 2 because i have to find the interval where the function is increasing or decreasing. i already know how to find the answer but i just got confused on

    asked by david on December 9, 2006
  6. Calculus (increasing/decreasing)

    Find the interval(s) where the function is increasing and the interval(s) where it is decreasing. (Enter your answers using interval notation. If the answer cannot be expressed as an interval, enter EMPTY or ∅.) f(x) = (5 −

    asked by Anna on February 19, 2018
  7. calc

    Consider the function below. (Round the answers to two decimal places. f(x) = 2x tan(x) -p/2 < x < p/2 (a) Find the interval where the function is increasing. Find the interval where the function is decreasing. (b) Find the local

    asked by bella on April 4, 2010
  8. Algebra 2

    Find the values of the inverse function in radians. sin^-1(0.65) a. 0.71+2pi n and -0.71+2pi n b. 0.71+2pi n and -3.85+2pi n c. 0.86+2pi n and -0.86 +2pi n d. -0.61+2pi n and 2.54+2pi n 2. tan^-1(0.09) a.-0.09+2pi n b. no such

    asked by Fading on May 21, 2017
  9. algebra

    Im having a hard time figuring out this problem: Use the function, y=-(x+1)^2 +2, to answer the following parts. Find the y-intercept y=-(0+1)^2 +2 y=-(1)^2 +2 y=-1+2 y=1 is my answer Find the x-intercept 0=-(x+1)^2 +2

    asked by Mike on May 4, 2011
  10. college algebra

    Given the following quadratic equation, find;? a. the vertex b. the axis of symmetry c. the intercepts d. the domain e. the range f. the interval where the function is increasing, and g. the interval where the function is

    asked by zachary on March 4, 2013

More Similar Questions