Average and instantaneous rates of change

Secant slopes versus tangent slopes, and why the derivative is a limit.

Standards:AP Calc AB · Unit 2

Try it: three questions

Real questions from the practice bank. Tap an answer to check it.

Question 1 of 3

A vehicle travels along a straight highway. Its position (in km) at time t (in hours) is given by s(t) = 2t² + 3t. Find the instantaneous rate of change (velocity) at t = 2 hours.

Question 2 of 3

A car travels along a straight road. Its position (in km) at time t (in hours) is given by s(t) = 2t² + 3t. Find the instantaneous rate of change (velocity) at t = 2 hours.

Question 3 of 3

A car's position is given by s(t) = 3t² + 2t, where s is in meters and t is in seconds. Find the instantaneous rate of change (velocity) at t = 4 seconds.

How this fits in

Average and instantaneous rates of change is one skill in the Intro to Calculus unit. Students read the unit lesson, then earn a bronze, silver, or gold medal on their last 10 answers. Medals never go down. A mastered unit comes back for review after 1, 3, 7, 16, and 35 days so it stays learned.

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