This week, we learned a couple new things, but they were parts of things we already knew. We learned how to find the original function from its derivative at a specific point. We already knew how to find original functions from derivatives, but I didn't know how to find the exact original function at a specific point. It's pretty simple, since you only have to plug values in and solve for the constant, so it wasn't super hard to learn.
The next new thing we learned about was how to make a slope field. For me, this sounded really complex until it was explained. To make a slope field, you really just need to know how to do simple math equations and then be able to graph something. For example, if you were asked to make a slope field for the function whose derivative was 2x+1, it's easiest to set up a table of x values that looks like this:
After you've set up a table, you just need to plug the x values into dy/dx. The value you get for dy/dx, is the slope of the tangent line at a specific point on the original function. After you have the values, you graph them like this:
The next new thing we learned about was how to make a slope field. For me, this sounded really complex until it was explained. To make a slope field, you really just need to know how to do simple math equations and then be able to graph something. For example, if you were asked to make a slope field for the function whose derivative was 2x+1, it's easiest to set up a table of x values that looks like this:
After you've set up a table, you just need to plug the x values into dy/dx. The value you get for dy/dx, is the slope of the tangent line at a specific point on the original function. After you have the values, you graph them like this:
From the graph, you can get an estimate of what the function will look like through any point.