Example Problem 1. Definition of Derivative

University
Rice University
Course
Preparing for the AP Calculus AB Exam
Pages

1

Academic year

2022
Author

FredCy
Views

84

p {margin: 0; padding: 0;} .ft00{font-size:20px;font-family:Arial;color:#000000;} .ft01{font-size:18px;font-family:ArialMT;color:#000000;} .ft02{font-size:18px;line-height:23px;font-family:ArialMT;color:#000000;} Definition of Derivative. Example Problem 1 Let's consider a function f. We'll plot the function on the standard coordinate plane andconsider the slopes of its tangent lines at various points. Basically, we are going to order the slopes of the lines tangent to the graph of f at givenpoints from least to greatest. Of course, one can be negative and one can be positive. But it is best to start drawingtangent lines. When choosing between two options, it is best to choose the one withthe greatest potential. Let's look at the graph of f and see where its slope is the steepest. The steepest slopeis at point D, so we'll put a dot there. Next, let's draw lines that are tangent to the graphat A, B and C. Let's say we have a negative slope at A and B, but not at C; therefore Cwill come third in our list. Finally, since all four lines in our diagram have positiveslopes, D will come last in our list. Now we are looking at the graph between B and C. You will notice that at C, the slopeof the line is zero (or horizontal). This means that C is the only point on the graph witha horizontal tangent, which means that it must be point 3 on our number line. Next, wesee that B has a positive slope and no horizontal tangent point. This means that Bmust be point 2 on our number line. Finally, A has no slope, so it must be point 1 onour number line. Therefore, the answer to this question is D, A, C, B.