Graph the function y = x 4 + 5x 3 – 6x 2 – 13x – 20
AP Calculus AB Name: __________________________________
Mr. Kerrigan
Graphing Calculator Skills Practice
Round all of your answers to three decimal places (AP standard).
Graph the function f (x) = x 4 + 5x 3 – 6x 2 – 13x – 20.
1. Find an appropriate viewing window that shows the graph’s important characteristics.
| |What window did you choose? |Sketch the graph you see. |
| |Xmin= |[pic] |
| |Xmax= | |
| |Xscl= | |
| |Ymin= | |
| |Ymax= | |
| |Yscl= | |
2. Find f (2).
3. Find the roots (zeros) of f.
Store one root as A and the other as B.
4. Find the value of (A + B) 2, using the [exact] stored values from your calculator
(not the rounded answers from #3).
5. Find the y-intercept of f.
6. Find the absolute minimum value of f (x).
What x-value yields this minimum?
7. There is only one relative maximum for f (x). What is it?
What x-value yields this maximum?
Keeping the graph of f, graph g (x) = 10x – 60 on the same axes.
Make the graph of g a bold line. You should now see the graphs of f and g.
8. Find all value(s) of x for which f (x) = g (x).
9. Find all value(s) of x for which f (x) ≤ g (x).
Give your answer in interval notation.
10. Find all value(s) of x for which f (x) = 50.
12. Find all value(s) of x for which f (x) > 50.
Give your answer in interval notation.
ANSWERS
|1. |Answers vary. Minimum requirements below. |Answers vary. Sample answer below. |
| |Xmin2.21 | |
| |Xscl=anything | |
| |Ymin0 | |
| |Yscl=anything | |
2. f (2) = -14
3. zeros (A and B): -5.755 and 2.212
4. (A + B) 2 = 12.548
5. y-intercept: f (0) = -20
(#5 is the same skill as #2. You just need to know that the y-intercept is where x = 0.)
6. absolute minimum: -130.722
when x = -4.274
7. relative maximum: -15.280
when x = -0.649
8. f (x) = g (x) for x = -4.940 and -3.025
9. f (x) ≤ g (x) for x in the interval [-4.940, -3.025]
(You didn’t need to do anything else in your calculator here. Use #8 and the graph to answer.)
10. f (x) = 50 for x = -5.969 and 2.680
(#10 is the same skill as #8. You need to make Y3 = 50 and find the intersection with Y1)
11. f (x) > 50 for x in the interval (-∞, -5.969) ( (2.681, ∞)
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