CK-12-Pre-Calculus Concepts

14.8. Instantaneous Rate of Change http://www.ck12.org

Guided Practice

1. Sketch a complete cycle of a sine graph. Estimate the slopes at 0,π 2 ,π,^32 π, 2 π.


2. Logan travels by bike at 20 mph for 3 hours. Then she gets in a car and drives 60 mph for 2 hours. Sketch both
   the distance vs. time graph and the rate vs. time graph.


3. Approximate the slope ofy=x^3 at( 1 , 1 )by using secant lines from the left. Will the actual slope be greater or
   less than the estimates?
   Answers:


4. 
   

TABLE14.13:

x Slope

0 1

π 2 0

π -1

32 π 0

2 π 1

You should notice that these are the exact values of cosine evaluated at those points.

2. Distance vs. Time: