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Part 2: Free Response Communicate your thinking clearly and completely. 12. We all “know” that the body temperature of a healthy person is 98.6°F
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IOWA 4-H PROJECT HOT SHEET Pass it on! ... •Visit a local meat locker or local grocery meat case to observe preparation and ... display showing what you’ve
The IB Diploma Programme (DP) is a rigorous, academically challenging and balanced programme of education designed to prepare students aged 16 to 19 for success at
About This Collection vi. Questions. 1. 1969 AP Calculus AB Exam, Section 1. 1. 1969 AP Calculus BC Exam, Section 1. 10. 1973 AP Calculus AB Exam, Section 1. 20 ... solve that question. There are often alternative approaches that produce the same cho
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submitted by email to [email protected]. K12T06. Single Variable Calculus: Early Transcendentals, Sixth Edition. James Stewart .... Answers to Odd -Numbered Exercises A63. INDEX. A112 x. ||||. CONTENTS ... Calculus, Sixth Edition, is similar
5 Chapter 1. Exam Format, Grading, and Tips 1.1. Exam Format Figure 1-1 shows the format of the AP Calculus exam. The exam takes 3 hours and 15
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10. We all know that the body temperature of a healthy person is 98.6 °F. In reality, the actual body temperature of individuals varies. Here is a back-to-back
Page 3 6. We all “know” that the body temperature of a healthy person is 98.6°F. In reality, the actual body temperature of individuals varies
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AP Calculus Project 4 - Curve Sketching
Name________________________
You will be in a group of 2 to 4. You will be given a series of functions that must be accurately sketched with attention paid to roots, extrema, critical points, inflection points, and end behavior.
Grading: Use of class time:
10 points
Example Curve:
10 points
Guided Practice Curve:
10 points
Grab Bag Curve 1 (given f(x)):
10 points
Grab Bag Curve 2 (given fʼ(x) & f”(x)):
10 points
Detail of diagrams:
20 points
Explanation of Calculus:
20 points
Quality of writing (complete sentences) 10 points Total:
100 points
Part 1
Part 2
Part 3
Part 4
Part 5
Part 6
Curve Sketching part 1 Steps Original function #1 Find the x and y intercepts Find any red flags in the domain and state if they create any vertical asymptotes Find the end behavior to the function. Find the first derivative Find the critical points using the first derivative Find the intervals of increasing and decreasing using the first derivative State ordered pairs for all minimums and maximums by using the intervals of increasing/decreasing and the original function Find the second derivative Find the inflection points using the second derivative Find the intervals of concavity using the second derivative State the ordered pairs of the points where concavity changes occur using the intervals of concavity and the original function Graph in the following order: - intercepts - vertical asymptotes - min’s and max’s - inflection points - now connect the dots keeping concavity and end behavior in mind.
Sketch a complete graph without the calculator. Work f(x) = 3x2 – x – 1
Curve Sketching part 2 Steps Original function #2 Find the x and y intercepts Find any red flags in the domain and state if they create any vertical asymptotes Find the end behavior to the function. Find the first derivative Find the critical points using the first derivative Find the intervals of increasing and decreasing using the first derivative State ordered pairs for all minimums and maximums by using the intervals of increasing/decreasing and the original function Find the second derivative Find the inflection points using the second derivative Find the intervals of concavity using the second derivative State the ordered pairs of the points where concavity changes occur using the intervals of concavity and the original function Graph in the following order: - intercepts - vertical asymptotes - min’s and max’s - inflection points - now connect the dots keeping concavity and end behavior in mind.
Sketch a complete graph without the calculator. Work f(x) = x3 – 6x2 +9x + 1
Curve Sketching part 3 Steps Original function #3 Find the x and y intercepts Find any red flags in the domain and state if they create any vertical asymptotes Find the end behavior to the function. Find the first derivative Find the critical points using the first derivative Find the intervals of increasing and decreasing using the first derivative State ordered pairs for all minimums and maximums by using the intervals of increasing/decreasing and the original function Find the second derivative Find the inflection points using the second derivative Find the intervals of concavity using the second derivative State the ordered pairs of the points where concavity changes occur using the intervals of concavity and the original function Graph in the following order: - intercepts - vertical asymptotes - min’s and max’s - inflection points - now connect the dots keeping concavity and end behavior in mind.
Sketch a complete graph without the calculator. Work f(x) = 2x4 + 4x3
Curve Sketching part 4 Steps Original function #4 Find the x and y intercepts Find any red flags in the ! domain and state if they create any vertical asymptotes Find the end behavior to the function. Find the first derivative Find the critical points using the first derivative Find the intervals of increasing and decreasing using the first derivative State ordered pairs for all minimums and maximums by using the intervals of increasing/decreasing and the original function Find the second derivative Find the inflection points using the second derivative Find the intervals of concavity using the second derivative State the ordered pairs of the points where concavity changes occur using the intervals of concavity and the original function Graph in the following order: - intercepts - vertical asymptotes - min’s and max’s - inflection points - now connect the dots keeping concavity and end behavior in mind.
Sketch a complete graph without the calculator. Work 1 f (x) = 2 x
Curve Sketching part 5 Steps Original function #8 Find the x and y intercepts Find any red flags in the ! domain and state if they create any vertical asymptotes Find the end behavior to the function. Find the first derivative Find the critical points using the first derivative Find the intervals of increasing and decreasing using the first derivative State ordered pairs for all minimums and maximums by using the intervals of increasing/decreasing and the original function Find the second derivative Find the inflection points using the second derivative Find the intervals of concavity using the second derivative State the ordered pairs of the points where concavity changes occur using the intervals of concavity and the original function Graph in the following order: - intercepts - vertical asymptotes - min’s and max’s - inflection points - now connect the dots keeping concavity and end behavior in mind.
Sketch a complete graph without the calculator. Work 6 6 f (x) = 2 " x x
Curve Sketching 6 Steps Original function #9 Find the x and y intercepts Find any red flags in the domain and state if they create any vertical asymptotes Find the end behavior to the function. Find the first derivative Find the critical points using the first derivative Find the intervals of increasing and decreasing using the first derivative State ordered pairs for all minimums and maximums by using the intervals of increasing/decreasing and the original function Find the second derivative Find the inflection points using the second derivative Find the intervals of concavity using the second derivative State the ordered pairs of the points where concavity changes occur using the intervals of concavity and the original function Graph in the following order: - intercepts - vertical asymptotes - min’s and max’s - inflection points - now connect the dots keeping concavity and end behavior in mind.
Sketch a complete graph without the calculator. Work f(x) = sin x + cos x from x = 0 to 2π
