Mr. Shaddick

Congratulations!

Congratulations to everyone on a fantastic year!  Enjoy your summer - and we'll see you back at DCVI in the fall ... except for those of you who have done your time ... have a great time at grad, be safe, and best of luck in your post-secondary studies.

-Mr. Shaddick

MCV 4U - June 3, 2009

Topic:  Intersections of Lines and Planes

Assigned work:
pg. 292 - 1bde, 2a, 4ab i), 5b, 6, 8, 9a

MCV 4U - May 21, 2009

Topic:  Applications of Dot Product and Cross Product in 3-Dimensions

pg. 192 - 1c, 2, 4, 9b, 10, 11, 14, 18, 19

MCV 4U - May 12, 2009

Dot Product and Geometric Vectors

Complete 1, 2be, 3, 5, 6 geometric, 13 on the handout.

MCV 4U - April 17, 2009

Topic:  Derivatives of other Logarithmic and Exponential Functions

Assigned work:
pg. 534
- eop of 1-3, 5
- 7-9, 10bd, 11

MCV 4U - April 16, 2009

Topic:  The Natural Logarithm

Assigned work:
pg. 527
adfj parts of 1,2, 7, 8, 13
14, 15, 23, 24
Achievement Check

MCV 4U - March 27, 2009

Topic:  Investigating Derivatives

First, revisit how to sketch the derivative of ANY curve. 

1. Draw a quick sketch to estimate what the derivative of the curve will look like.
2. Click on the show derivative button to see the derivative of the curve.
3. Click to hide the derivative and drag points on the curve.
4. Draw a quick sketch and check your answer.
5. How is the sign of the derivative related to the original function?  the zeros?
6. Discuss with your partner what the second derivative graph would look like.

Now, remember the sine function?  Today, we'll be exploring the derivative of the sine function.

1. Begin by opening the graph of f(x)=sin(x) in degrees.  
2. Discuss with your partner how this represents circular motion.
3. Move the 't' slider to observe the tangent line at various points on the curve.
4. Estimate the slope at 0, 90, 180, 270, 360 degrees.  (You can zoom in by selecting a rectangular area with the left mouse button ... although I have no idea how to do this on a Mac.  To zoom out, hold shift and the left mouse button.).
5. Sketch these points on a graph.  What kind of function do you think it will produce?
6. What is the slope at 0 degrees (approximate to the nearest degree)?

Ok ... I'll admit it.  This next interactive tool made me salivate:

1. Thanks to the University of Virginia, here is an interactive derivative tool.
2. First, select the x^2 function. 
3. Change the window settings to -10 to 10.
4. Click to show the tangent line. 
5. Move the orange circle, P, along the curve to see how the tangent slope (derivative) at P changes.
6. To observe how the secant line approaches the tangent line as the x-coordinate of Q approaches the x-coordinate of P, click on secant line and drag Q towards P.
7. De-select the secant line
8. Select the sin x function.
9. Change the window settings to -1 to 7. 
10. What units are angles measured in?
11. Find the tangent slope (derivative) at various points and sketch a graph.
12. What is the slope at 0 degrees?  (ahhh ... the beauty of radians.)
13. What function represents the derivative of f(x)=sin(x)?

Here is a visual display of the result:

1. Open the Interactive Tutorial by clicking on the box that orders you to do so.
2. Drag the tangent position slider to observe a sketch of the derivative of f(x)=sin(x)
3. What function is it?

Lastly, let's examine the second derivative in this Japanese-produced applet:

1. Read the introduction for an explanation of the applet.
2. Scroll down to the applet below.
3. Drag the red dot to see what the derivative and second derivative of f(x)=sin(x) look like.
4. What function is the second derivative?
5. Select the cosine graph from the drop down menu and repeat.
6. What is the first derivative function and second derivative function of f(x)=cos(x).

... and let's summarize our findings together on the board.

MCV 4U - Students Beyond Borders

For those out of the country at the moment, I can assure you that I will be checking the blog with regularity over the next week to assist you with any questions that you many have regarding the assigned work (we did more optimization problems, the second derivative test, and concavity).  In other words, do not save all of your questions until the Monday after the March Break.  If you are asking questions now (using the comment section of the blog), you should be prepared to make up the test after school.  We can go over the smaller, more specific, problems at lunch and during period 5 when you return.

Enjoy March Break!

MCV 4U - March 10 & 11

Topic:  Second Derivative and Concavity

Assigned work:
pg. 331 - 8aef, 12a, 15cf

Test review questions:
pg. 336 - 20ef, 21, 24, 25, 27, 29c, 30f
pg. 416 - 18a
pg. 421 - 20bi, 21b, 26, 27, 28, 29, 31

MCV 4U - March 6 & 9, 2009

Topic:  More Optimization Problems

Assigned work:
pg. 310 - 9, 10, 12, 14, 15, 22
pg. 320 - 8, 10, 12, 13, 15, 18
pg. 401 - 4, 7, 12