Section 2.1 The Tangent and Velocity Problems AP Calculus September 10, 2009 Berkley High School, D2B2

The importance of slope Imagine we are going to model an everyday phenomenon like motion. Calculus, Section 2.1

The importance of slope Imagine we are going to model some everyday phenomenon like motion. We’ll start with an easy example: “A randomly selected calculus teacher enters I-75 at exit 62 (11 Mile Road). He heads north at a speed of 65 miles per hour.” Make an equation that shows mile mark to traveled to (M) as a function of hours (H) traveled. Calculus, Section 2.1

The importance of slope Calculus, Section 2.1

The importance of slope In this function, what does slope represent? In a position equation, the slope represents “velocity.” Calculus, Section 2.1

Graph it. Calculus, Section 2.1

What if? Calculus, Section 2.1

Can we find the slope/velocity? Calculus, Section 2.1

Using secant line as approximation of slope, from (0, 0) to (2.5, 150) Calculus, Section 2.1

Using secant line as approximation of slope, from (0, 0) to (2.5, 150) Calculus, Section 2.1

Using secant line as approximation of slope. From (2, 136) to (2 Calculus, Section 2.1

Approximation of slope, from (2.25, 144) to (2.5, 150) Calculus, Section 2.1

Using Y= and Tables If you feel comfortable with finding slope by hand, you might consider using the calculator’s ability to do many calculations simultaneously. Demonstration… Calculus, Section 2.1

Using Y= and Lists Step 1: Put the function in question in Y= Calculus, Section 2.1

Using Y= and Lists Step 2: Put sample X value in a list Calculus, Section 2.1

Using Y= and Lists Step 3: Put as the header to a different the slope formula Calculus, Section 2.1

Assignment Section 2.1, Exercises 1-9 odd Calculus, Section 2.1