Results 1 to 3 of 3

Math Help - Extrema on interval?

  1. #1
    Senior Member
    Joined
    Dec 2010
    From
    CPT
    Posts
    302

    Extrema on interval?

    Find the critical numbers of the function. I have two(?).

    1. x square root(4-x) (This is what I did)

    square root(4-x)(1)+(x) ((4-x))/((2 square root(4-x))

    square root(4-x)+((1x))/((2 square root 4-x))

    I think I differentiated for it but how would I factor to find the critical numbers?

    2. sin^2(x)+cos(x)

    cos^2(x)-sin(x)

    Here I have the same issue as my top problem
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,706
    Thanks
    625

    Re: Extrema on interval?

    Hello, homeylova223!

    What intervals are given?


    (1)\;\;f(x) \:=\:x\sqrt{4-x}

    Differentiate: . f'(x) \;=\;1\cdot(4-x)^{\frac{1}{2}} + x\cdot\tfrac{1}{2}(4-x)^{-\frac{1}{2}}(-1)

    We have: . \sqrt{4-x} - \frac{x}{2\sqrt{4-x}} \;=\;0

    Assume x \ne 4
    Multiply by 2\sqrt{4-x}\!:\;\;2(4-x) - x \:=\:0

    . . Therefore: . \boxed{x \:=\:\tfrac{8}{3}}




    (2)\;\;f(x) \:=\:\sin^2\!x+ \cos x

    Differentiatte: . 2\sin x\cos x - \sin x

    We have: . \sin x(2\cos x-1) \:=\:0


    And we have two equations to solve:

    . . \sin x \:=\:0 \quad\Rightarrow\quad \boxed{x \:=\:n\pi}

    . . 2\cos x-1\:=\:0 \quad\Rightarrow\quad \cos x \:=\:\tfrac{1}{2} \quad\Rightarrow\quad \boxed{x \:=\:\pm\tfrac{\pi}{3} + 2\pi n}

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Dec 2010
    From
    CPT
    Posts
    302

    Re: Extrema on interval?

    Thanks your response was very helpful. Also the only interval given was for my second questions and it was between 0 and 2 pi I think.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Extrema on an Interval
    Posted in the Calculus Forum
    Replies: 5
    Last Post: February 5th 2010, 02:54 AM
  2. Replies: 1
    Last Post: June 9th 2009, 09:29 PM
  3. Extrema on an interval find critical numbers
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 9th 2009, 03:13 PM
  4. Extrema of a closed interval??
    Posted in the Calculus Forum
    Replies: 7
    Last Post: October 21st 2008, 06:45 PM
  5. Extrema on a closed interval
    Posted in the Calculus Forum
    Replies: 5
    Last Post: October 13th 2008, 06:08 PM

Search Tags


/mathhelpforum @mathhelpforum