Problem Solving Practice

1
Problem Solving Practice

• Chapter 2 Review

2
Mr. Garrison took the derivative of f(x) and
found that

• What could f(x) have been?

3
The following is a graph of f(x). Sketch a graph
of f(x) and describe the key features
4
Below is a graph of f(x). Draw a rough sketch of
the shape of f(x), and explain why it has this
shape
5
Problem Applications of Design

• You are being asked to design a new pop can. The
  shape must be a cylinder with a volume of 355
  cubic cm, but in order to save on materials, the
  surface area must be as small as possible.
• What are the dimensions of this new pop can?

6
Problem Largest Area

• A triangle is inscribed inside of a circle. What
  is the largest possible area for this triangle if
  the radius of the circle is 20 cm?

7
Problem Decelerating Car

• The distance travelled by a car is given by the
  following equation, with s in metres and t in
  seconds
• How far will the car travel before it stops?

8
Problem Accelerating Object

• An object is thrown up into the air, and its
  height vs. time is given by
• What is the acceleration of this object? (the
  change in velocity per second)

9
Problem How far will this car travel in 30
seconds?

• It is accelerating at 3 metres per second per
  second
• It starts off with a velocity of 20 metres per
  second
• Use derivatives to determine the distance
  travelled in 30 seconds

10
Chapter 2 Summary

• What is the meaning of a derivative?
• Where do all of the derivative rules come from?
• How does the derivative help us find the maximum
  or minimum value of a function?
• Practice Pg. 110, 5, 9, 12, 15, 22, 29
• Practice test Pg. 114, 1-11 (time yourself for
  50 minutes)