Reflection of this Semester
One skill that I really improved at this year was finding derivatives. At first I had a problem with the overall idea and conceptualizing what derivatives are used for. Eventually, through all of the repetition I finally had a way of thinking of it. I did not really think of derivatives as literally graphing the slope of a function where if the slope is 3, the derivative will pass through that point. Once I realized this, I started to look at them in a different way and understand what certain curves meant. Although I did not do very well on my derivative test, I now understand them much better. For example, if I wanted to find the derivative of (3x2+x3)/2x, then I would start by writing out the quotient rule equation.
3. Then, once I got this far I found the derivative of this function to be 3/2 + x.
I used to have a lot of trouble remembering the original quotient rule equation. Now, I have committed it to memory and completely can visualize the steps.
One problem solving skill that I have improved at this year was generating ideas. I know that this is one skill that I struggled with a lot last year when we had more guidance through each problem. Now that we are being introduced more complicated problems and trying to figure a lot of them out on our own, I am starting to get good at generating ideas. Most times I am introduced a new problem I try to think about it in as many ways as possible. This usually looks like me drawing pictures, rewriting the problem, or asking a different question in order to advance further in the problem and understand it from all angles.
- (f’g-g’f)/g2 Then, I would find out what each variable is. f=3x2+x3 g=2x. To find f’ and g’, I need to take the derivative of these variables on their own. f’=6x+3x2 g’2.
- Next, I plugged these numbers into the equation. (12x2+6x3)+(-6x2-2x3)/4x2
3. Then, once I got this far I found the derivative of this function to be 3/2 + x.
I used to have a lot of trouble remembering the original quotient rule equation. Now, I have committed it to memory and completely can visualize the steps.
One problem solving skill that I have improved at this year was generating ideas. I know that this is one skill that I struggled with a lot last year when we had more guidance through each problem. Now that we are being introduced more complicated problems and trying to figure a lot of them out on our own, I am starting to get good at generating ideas. Most times I am introduced a new problem I try to think about it in as many ways as possible. This usually looks like me drawing pictures, rewriting the problem, or asking a different question in order to advance further in the problem and understand it from all angles.