3.6 Day 2 Example 2
3.6 Day 2 Example 2
Curve Sketching Polynomials
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00:00:23
What is always the domain of a polynomial function?
 Positive Numbers
 All Real Numbers
 Imaginary Numbers
 Natural Numbers

00:00:35
What is the end behavior for this function?
 Rising, left to right
 Falling, left to right
 Pointing upwards on both sides
 Pointing downwards on both sides

00:00:49
What is the yintercept for this function?
 (0, 5)
 (0, 0)
 (0, 5)
 (5, 0)

00:01:45
When do you use the plus or minus in front of a radical?
 All radicals
 Even powers
 Odd Powers
 Never

00:02:10
What is the derivative, f'(x)?
 f'(x) = x^5  5
 f'(x) = 5x^4  5
 f'(x) = 5x^4
 5x^4  5x

00:02:30
What are the critical numbers?
 c= 0
 c=1
 c=  1
 c= 4
 c= 5
 c = 5
 c= 4

00:03:16
What happens in the original graph when the derivative changes from positive to negative?
 Minimum
 Maximum

00:03:50
What is the yvalue of the maximum that occurs at x = 1?
 y = 4
 y = 4
 y = 0

00:04:01
What is the yvalue of the minimum that occurs at x = 1?
 y = 0
 y = 4
 y = 4

00:04:22
What is an inflection point?
 Where the function changes concavity
 Extrema
 Where the function changes sign
 Where the function is increasing

00:04:35
What is the second derivative, f''(x)?
 f''(x) = 5x^3
 f''(x) = 20x^3
 f''(x) = 20x^3  5
 f''(x) = 5x^3  5

00:04:45
What is the fence post for the second derivative test?
 0
 1
 1
 20
 3

00:04:58
When the second derivative is negative, what does that tell you about the original function?
 Increasing
 Decreasing
 Concave Up
 Concave Down

00:05:07
When the second derivative is positive, what does that tell you about the original function?
 Increasing
 Decreasing
 Concave Up
 Concave Down

00:06:35
What does the graph look like when the function is concave down?
 Increasing
 Decreasing
 Facing Up
 Facing Down

00:06:56
Now you are ready to try on your own. You have been performing first and second derivative tests for three weeks. Now you are sketching the graph in addition. Do not use your graphing calculator!
 No, I am probably going to use my graphing calculator and then regret that decision when I have a quiz/test where I am unable to use it
 Yes, I understand and will not use my graphing calculator
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