Exploring Derivatives and Their Role in Curve Analysis

What did Mr. Snickerdoodle buy to fulfill his racecar driving ambitions?

• A leather furnished golf cart

• A motorcycle

• A bicycle

• A sports car

What is Mr. Snickerdoodle's favorite number?

• 10

• 5

• 12

• 7

How is velocity defined in the context of this problem?

• Change in distance over change in speed

• Change in speed over change in distance

• Change in time over change in position

• Change in position over change in time

What is the position function f(x) for Mr. Snickerdoodle's golf cart?

• f(x) = 2x

• f(x) = x^3

• f(x) = x^2

• f(x) = x

What is the slope of a line typically found by?

• Taking the average of two points on the line

• Taking the difference of y-values over the difference of x-values

• Taking the sum of two points on the line

• Taking the product of two points on the line

What is the term used to describe getting closer and closer to something in mathematics?

• Limit

• Integral

• Derivative

• Function

What is the formula for the slope of the tangent line at a point x?

• The limit as h approaches zero of f(x+h) minus f(x) all over h

• The limit as h approaches zero of f(x+h) plus f(x) all over h

• The limit as h approaches zero of f(x) plus f(x+h) all over h

• The limit as h approaches zero of f(x) minus f(x+h) all over h

What is the derivative of the function f(x) = x^2?

• 2x^2

• 2x

• x^2

• x

What is Mr. Snickerdoodle's speed at 10 seconds?

• 25 feet per second

• 15 feet per second

• 20 feet per second

• 10 feet per second

What is Mr. Snickerdoodle's speed in miles per hour?

• 15.8 miles per hour

• 13.6 miles per hour

• 12.4 miles per hour

• 10.2 miles per hour