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Math Help - Curve Sketching

  1. #1
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    Curve Sketching

    I am having difficulty with this problem, I believe I am doing it right, however my answers and the book's don't correspond.

    F(X)= (X-2)^3

    I used the chain rule and brought out the 3 and got:

    3(X-2)^2 (1) = 3(X-2)^2 So my X zero value would be just X= 2 if I am not mistaken. I then used a number line and put 2 on it and used the factors (3 and (X-2) ) to see where it's positive and negative. 3 Is always positive on the number line, however X-2 is negative at >2 so I got an interval of increase/ decrease of (-Infiniity , 2) Function is decreasing , (2, +infinity) function increasing, however the book is saying that the X is increasing for all. What am I doing wrong?
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  2. #2
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    Quote Originally Posted by kdogg121 View Post
    I am having difficulty with this problem, I believe I am doing it right, however my answers and the book's don't correspond.

    F(X)= (X-2)^3

    I used the chain rule and brought out the 3 and got:

    3(X-2)^2 (1) = 3(X-2)^2 So my X zero value would be just X= 2 if I am not mistaken. I then used a number line and put 2 on it and used the factors (3 and (X-2) ) to see where it's positive and negative. 3 Is always positive on the number line, however X-2 is negative at >2 so I got an interval of increase/ decrease of (-Infiniity , 2) Function is decreasing , (2, +infinity) function increasing, however the book is saying that the X is increasing for all. What am I doing wrong?
    (x - 2)^2 is always greater than or equal to zero. Note that the square of a negative is a positive. So if (x - 2) is negative, the square of (x - 2) will be positive ......
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  3. #3
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    Quote Originally Posted by kdogg121 View Post
    I am having difficulty with this problem, I believe I am doing it right, however my answers and the book's don't correspond.

    F(X)= (X-2)^3

    I used the chain rule and brought out the 3 and got:

    3(X-2)^2 (1) = 3(X-2)^2 So my X zero value would be just X= 2 if I am not mistaken. I then used a number line and put 2 on it and used the factors (3 and (X-2) ) to see where it's positive and negative. 3 Is always positive on the number line, however X-2 is negative at >2 so I got an interval of increase/ decrease of (-Infiniity , 2) Function is decreasing , (2, +infinity) function increasing, however the book is saying that the X is increasing for all. What am I doing wrong?
    By the way, the book is wrong. The function is NOT increasing at x = 2. There is a stationary point of inflexion at x = 0. The function is neither increasing or decreasing at x = 2.

    The function is increasing over the intervals (-oo, 2) and (2, oo).
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  4. #4
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    Thanks guys, I forgot that the factor was squared so this would make any number positive.
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