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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