Determine points on the graph y= x^(3/2) - x^(1/2) where the tangent line is parallel to y=x+3.
This question is in the unit of my manual about derivatives, which gives me the idea that I have to somehow use this. I know the slope of y=x+3 is 1, which means the tangent lines of the points on that graph will have a slope of 1, but I don't know how to work backward from there. Any hints as to the process would be helpful. There are no relevant examples in my manual at all.
Thank you for the replies. Is there a specific rule that allows me to ignore the denominator in the 2nd-3rd step? I would have thought I needed to multiply all the numerators by the denominator in order to go on to the next step. This is probably something simple that I'm missing, but would someone enlighten me?
Alright, thank-you, I suppose that makes sense. Now, I am just wondering for the step where the entire equation is squared, is there also a certain rule that allows me to manipulate the equation in that way?
Alright, thank-you. I guess I was just uneasy about accepting that with the denominator still in mind. However, I suppose that if the common denominator is irrelevant then this should not matter. Thank-you for all of your clarification.