2. Differentiation(COLON) Definition and Fundamental Properties

Defining Average And Instantaneous Rates Of Change At A Point — Quiz

Test your understanding of defining average and instantaneous rates of change at a point with 5 practice questions.

Practice Questions

Question 1

What does the average rate of change of a function $f$ from $x=a$ to $x=b$ represent?

Question 2

What quantity gives the instantaneous rate of change of a function $f$ at $x=a$?

Question 3

A function has values $f(2)=5$ and $f(6)=17$. What is the average rate of change from $x=2$ to $x=6$?

Question 4

Which expression represents the derivative of $f$ at $x=a$ using the limit definition?

Question 5

If the graph of $f$ has a tangent line that is horizontal at $x=a$, what is $f'(a)$?