This week we dove into the world of derivatives. It's been a lot of fun.
We started the week off with 3.1 discussing what a derivative is. The derivative of f with respect to x is the function: limit as h approaches 0 f'(x)=f(x+h)-f(x)/h. It looks like a lot of junk but it really is a lot of fun. The four steps to solve go as folllows:
1. Find f(x+h)
2. Write f(x+h)-f(x), the simplify
3. Write f(x+h)-f(x)/h, then simplify
4. Take the limit as h approaches 0 of f(x+h)-f(x)/h
And WALLAH! the f'(x) equation.
f'(x) is the derivative of f.
We had homework over this concept and I totally got it and I felt great! I had a little confusion about the back of the worksheet, but understood it after we did the CCC in class the next day. I just confused myself and made it more complicated than it really was.
The Lab 6 was very helpful to really see how the derivative function was related to the original function. Using Desmos, we answered questions about each graph like where the graph was rising on the graph of the original function and where the graph is above the x-axis, and where the graph of the function was decreasing and where it was below the graph on the derivative, where the minimum and maximum were on the original function graph and where the zeroes were on the graph of the derivative. It showed how the function is rising where the graph of the derivative is above the x-axis, is falling where the graph of the derivative is below the x-axis, and the maximum and minimum of the function is where the function of the derivative crosses the x-axis. By discovering this, the idea of how the graph of the derivative of a function and the function are related really clicked.
The ideas we discussed in class this week I feel like I really understand and that’s great.
We started the week off with 3.1 discussing what a derivative is. The derivative of f with respect to x is the function: limit as h approaches 0 f'(x)=f(x+h)-f(x)/h. It looks like a lot of junk but it really is a lot of fun. The four steps to solve go as folllows:
1. Find f(x+h)
2. Write f(x+h)-f(x), the simplify
3. Write f(x+h)-f(x)/h, then simplify
4. Take the limit as h approaches 0 of f(x+h)-f(x)/h
And WALLAH! the f'(x) equation.
f'(x) is the derivative of f.
We had homework over this concept and I totally got it and I felt great! I had a little confusion about the back of the worksheet, but understood it after we did the CCC in class the next day. I just confused myself and made it more complicated than it really was.
The Lab 6 was very helpful to really see how the derivative function was related to the original function. Using Desmos, we answered questions about each graph like where the graph was rising on the graph of the original function and where the graph is above the x-axis, and where the graph of the function was decreasing and where it was below the graph on the derivative, where the minimum and maximum were on the original function graph and where the zeroes were on the graph of the derivative. It showed how the function is rising where the graph of the derivative is above the x-axis, is falling where the graph of the derivative is below the x-axis, and the maximum and minimum of the function is where the function of the derivative crosses the x-axis. By discovering this, the idea of how the graph of the derivative of a function and the function are related really clicked.
The ideas we discussed in class this week I feel like I really understand and that’s great.