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Math Help - sign chart, finding intervals of increase, decrease?

  1. #1
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    sign chart, finding intervals of increase, decrease?

    (x+1)^5-5x-2
    f'(x)=5(x+1)^4-5
    x=-2,0
    if i make a sign chart, i would have to do all 4 factors (x+1) which means all negative signs would then be made positive.
    but in the answer section, it says between -2 and 0, the function is decreasing, which means in the sign chart, it should be negative....
    i hope im making sense..
    what am i overlooking here?
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  2. #2
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    Hi

    f'(x) = 5(x+1)^4-5 = 5x(x+2)[(x+1)+1]

    Since 5[(x+1)+1] > 0 the sign of f' is the same as x(x+2), therefore negative between -2 and 0
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  3. #3
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    hmm, can you explain how you factored out f'(x)=5(x+1)^4-5 to be 5x(x+2)[(x+1)^2+1]?
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  4. #4
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    f'(x) = 5(x+1)^4-5 = 5[(x+1)^4 - 1]

    (x+1)^4 - 1 = [(x+1)]-1 = [(x+1)-1][(x+1)+1] = (x+1-1)(x+1+1)[(x+1)+1] = x(x+2)[(x+1)+1]

    It is a matter of using a-b = (a-b)(a+b)
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