2.3 Estimating Derivatives of a Function at a Point

Adding on to previous lessons, another way to write derivatives is using the limit formula, where a is the point at which we want to take the derivative. 🎯

Sometimes, the College Board® will ask you to estimate the derivative based on a table or graph. These might seem really difficult at first, but there are some strategies to figuring out what they are looking for. It’s important to keep in mind that the derivative is the slope of the tangent line at a single point. 

If the problem has a table of x- and f(x)- values, then you should look back to the average rate of change formula that we discussed at the beginning of this unit. You are trying to approximate the slope of the tangent line at a point, so it’s most logical to find an average slope around that point. 

If you are asked to estimate the derivative based on a graph, it will almost always be a multiple-choice question. You’ll learn more about this in Unit 5 with Applications of Derivatives!