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Homework Help: Calculus

Posted by Tina on Friday, November 26, 2010 at 5:51pm.

Find the critical numbers of the function on the interval 0 ≤ θ < 2π. Small & large value

f(θ) = 2cos(θ) + (sin(θ))^2

• Calculus - Reiny, Friday, November 26, 2010 at 10:49pm

  let's take f '(Ø)
  f '(Ø) = -2sinØ + 2sinØcosØ
  = 0 for max/mins
  
  sinØ - sinØcosØ = 0
  sinØ(1 + cosØ) = 0
  sinØ = 0 or cosØ = -1
  Ø = 0,π,2π or Ø = 3π/2
  f(0) = 2+0 = 2
  f(π) = -2+0 = -2
  f(2π) = 2 + 0 = 2
  f(3π/2) = 0 + 1 = 0
  
  max value of the function is 2 when Ø = 0 or 2π
  min value of the function is -2 when Ø = 3π/2
  

• Calculus - Anonymous, Friday, October 26, 2012 at 9:44am

  2sinθcosθ-1=0
  

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