Thread: 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?

Originally Posted by kdogg121

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 ......

Originally Posted by kdogg121

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).

Thanks guys, I forgot that the factor was squared so this would make any number positive.