Calculus Help? BEST ANSWER?!?

This is what I think you are trying to convey:

You have two tables, each representing a function (y=x^2 and y=x^3)

For each table, one column shows the x values you listed above, and the second column lists the y values you get when you plug those into the function.

If this is correct, proceed to the solution below.

Since you seem like a motivated student I won't simply give you the answer. To solve this problem you need to use the definition of slope. Specifically, change in y over change in x. The best way to do this is to find the point in question (x=-1.0). Find the slope as it moves to this point from the left. This means take the y value at x=-1 and subtract from it the y value at x=-1.5. Then divide this by the change in x over this region (0.5). This is the slope to the left of -1.0. Now you will do the same thing to the right of -1.0. Subtract the y value at -1.0 from the y value at -0.5 and divide by 0.5. Now you have two slopes. One to the left of the point and one to the right. To find the average slope at the point, you simply take the average of these two values.

But you may be thinking, this value isn't the exact slope at x=-1.0, its just an estimate. Well you're right, this is what motivates the concept of derivatives. Imagine doing the same thing but now instead of estimating the slope on intervals of length 0.1 instead of 0.5 like you did in the above problem. Well, this would make the estimate of the slope slightly more accurate. Now imagine making the interval 0.001. Even more accurate. Derivatives allow you to know the exact slope at that point but until then you can only estimate.