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Math Help - f'(x) compared to g'(x) inequality problem

  1. #1
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    f'(x) compared to g'(x) inequality problem

    Assume f is differentiable for all x. The signs of f' are as follows.
    f'(x) {greater than sign} 0 on (-infinity,-40
    f'(x) {less than sign} 0 on (-4,6)
    f'(x) {greater than sign} 0 on (6, infinity)

    Supply the appropriate inequality for the indicated value of c. (The sign goes inbetween the { marks)
    Function
    g(x)=f(x)+5

    Sign of g'(c)
    g'(0) { } 0


    I think this question might involve moving the graph. If I take f(x) and move it up five....at least I think I should move it up five... will the derivative still have the same sign? Any ideas of what to do are greatly appreciated. Thanks for your help!!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by liz155 View Post
    Assume f is differentiable for all x. The signs of f' are as follows.
    f'(x) {greater than sign} 0 on (-infinity,-40
    f'(x) {less than sign} 0 on (-4,6)
    f'(x) {greater than sign} 0 on (6, infinity)

    Supply the appropriate inequality for the indicated value of c. (The sign goes inbetween the { marks)
    Function
    g(x)=f(x)+5

    Sign of g'(c)
    g'(0) { } 0


    I think this question might involve moving the graph. If I take f(x) and move it up five....at least I think I should move it up five... will the derivative still have the same sign? Any ideas of what to do are greatly appreciated. Thanks for your help!!
    Since g(x)=f(x)+5, g'(x)=f'(x), and so:

    g'(x) > 0 on (-infinity,-4)
    g'(x) < 0 on (-4,6)
    g'(x) > 0 on (6, infinity)

    so g'(0)<0

    RonL
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  3. #3
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    Thanks for you help. I see what you did.

    --Cori
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