Hi Again! Right now I'm taking derivatives in relation to curve sketching, and I just wanted to make sure I am doing these right. The first question is to determine using the first derivative where the graph of y = x is rising. (x^2)+1 This is what I have done so far: I tried to find the derivative using the quotient rule..... ((x^2)+1)(d/dx)(x)-(x)(d/dx)((x^2)+1) ((x^2)+1)^2 ((x^2)+1)(1)-(x)(2x) ((x^2)+1)^2 (-x^2)+1 ((x^2)+1)^2 That is the value I found for the first derivative, although I am unsure whether I have done it right or not. Then to find where the curve was rising I said that since the derivative must be greater than 0, the value I found for the derivative must be greater than zero. Then I tried solving that and I ended up with -x^2 + 1 > x^4 + 2x^2 + 2 and although I realize that that is not quite finished yet, it just doesn't seem right to me. I am obviously going wrong somewhere, but where I do not know. The second question asks you to determine where f(x) = x^2(1-x) is concave upward using the second derivative. This is what I did: (x^2)(d/dx)(1-x) + (1-x)(d/dx)(x^2) = (x^2)(-1) + (1-x)(2x) = (-3x^2) + 2x This is the first derivative I found using the product rule and the steps shown above. Then I found the second derivative to be -6x + 2 Have I found the derivatives correctly for these questions?????? It just seems like something is very wrong, mostly with the first question. Any help you guys can give me I would really appreciate. Thanks in advance.