3.2 Extrema & Function Analysis Name: 1
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1 Precalculus Write our questions and thoughts here! 3.2 Etrema & Function Analsis Name: 1 Absolute ma/min absolutel the. Relative ma/min a point on the function that is. Finding a ma/min means finding the of the point. The value helps ou with location of the point, but it is not the ma/min value. 1. Find the coordinate points of the etrema of each function and classif its tpe What is the minimum value of? 2. Closed Endpoint: 3. Open Endpoint: 3. Jump Discontinuit
2 Write our questions and thoughts here! 3.2 Etrema & Function Analsis 2 4. Finding a friendl window Function Analsis putting it all together! Domain: Vertical Asmptotes: (Nonremovable) Holes: (Removable) Absolute ma/min value: Local ma/min value(s) that are NOT absolute: Left End Behavior: Right End Behavior: Sketch a graph: Skillz Review: Solve or evaluate
3 3.2 Practice Etrema & Function Analsis Name: Pre Calculus Using the graph and/or the function s equation, find all of the following. Use Interval Notation when describing intervals. Sketch the graph if it is not given. Domain: Absolute ma/min value(s): 1. Local ma/min value(s) that are NOT absolute: Left Right Domain: Absolute ma/min value(s): 2. 9 Local ma/min value(s) that are NOT absolute: Left Right Domain: Absolute ma/min value(s): 3. Local ma/min value(s) that are NOT absolute: Left Right
4 Domain: Absolute ma/min value(s): Local ma/min value(s) that are NOT absolute: Left Right Domain: Absolute ma/min value(s): Local ma/min value(s) that are NOT absolute: Left Right Domain: Absolute ma/min value(s): 6. Local ma/min value(s) that are NOT absolute: Left Right Domain: Absolute ma/min value(s): 7. Local ma/min value(s) that are NOT absolute: Left Right
5 3.2 Application and Etension For 1 2, the etrema are listed for a function f along with the restricted domain. Find the absolute maimum value and absolute minimum value on the interval. DON T USE THE GRAPH! ; ; Etrema at: Etrema at: A rectangle has its base on the ais and its two upper corners on the parabola 12. a. Draw this scenario on the coordinate plane to the right, and draw a possible rectangle. b. Label the base and height of our rectangle in terms of. c. Find the function that represents the area of the rectangle. d. What is the largest possible area of this rectangle? (Hint: Use a calculator to graph and find the maimum!) e. At what value should the rectangle be drawn for the largest area? 4. Sketch (freehand) a graph of a function with domain all real numbers that satisfies all of the following conditions: a. There are no breaks in the graph (it is continuous). b. is decreasing on, 3 and on 4, c. is increasing on 1, 4 d. 4 7 e. 0 on 4, 0
6 5. Mr. Sullivan has hired ou to design a window in front of his house. His specifications are that it is to be a rectangular shape with a semi circle on top (see figure) and the perimeter of the window is 288 inches. He wants ou to create a window with the largest possible area that fits those specifications. a. Using r as the radius of the semi circle, label the top edge of the semicircle in terms of r. (Hint: What is the circumference of a circle?) b. Label the bottom of the window in terms of r. c. Label the height of the rectangular portion as H. d. Find H in terms of r. e. Label the area of the semi circle. Find an equation for. f. Label the area of the rectangle. Find an equation for. g. Find, the total area of the window. h. What is the largest area of the window? (3 decimal places and use correct units) i. What is the width of the bottom of the window to create this large area? (3 decimal places and use correct units)
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9. p(x) = x 3 8x 2 5x p(x) = x 3 + 3x 2 33x p(x) = x x p(x) = x 3 + 5x x p(x) = x 4 50x
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9. p(x) = x 3 8x 2 5x p(x) = x 3 + 3x 2 33x p(x) = x x p(x) = x 3 + 5x x p(x) = x 4 50x
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