Calculus Critical Points Jeopardy

1. Calculus Critical Points Jeopardy

2. Max/ Min – 10 points Use the graph below to state the Absolute Extrema.

3. Max/Min – 20 points State the x values of Relative Maximum.

4. Max/Min – 30 points State the x values of Relative Minimum

5. Max/Min – 40 points State the x values of ALL Relative Extrema.

6. Max/Min – 50 points State the x values of Relative & Absolute Extrema.

7. Derivative – 10 points f( x) = x3 – 6x2 + 12x – 5 f( x) = ?? Factored completely!

8. Derivatives – 20 points f( x) = 4x2 – 10x + 14 f ‘( 4 ) = ?

9. Derivative – 30 points F(x) = 3x4 – 4x3 -36x2 f ’(x) = 0 when x = ???

10. Derivatives – 40 points Use the Chain rule to take derivative. (Factor for additional 20 points) Y = (2x3 – 6x2 ) 4 Y ‘ = ?

11. Derivatives – 50 points Calculate and simplify the derivative.

12. Critical Points – 10 points State the critical point of f(x) = 4x2 – 16x - 12

13. Critical Points – 20 points State the 2 critical points of f(x) = x3 – 12x + 7

14. Critical Points – 30 points State the 2 critical points of f(x) = 2x3 + 3x2 – 12x + 8

15. Critical Points – 40 points State the critical points of f(x) = x4 – 2x2 + 1

16. Critical Points – 50 points State the critical points of f(x) = 3x4 + 16x3 + 18x2 - 12

17. Increasing/ Decreasing – 10 points For the curve below state the decreasing intervals

18. Increasing/ Decreasing – 20 points For the curve below [-2,2] state the increasing intervals.

19. Increasing/ Decreasing – 30 points Use the sign table below to state the Increasing intervals.

20. Increasing/ Decreasing – 40 points f( x) = x3 + 3x2 + 4 State the decreasing interval

21. Increasing/Decreasing – 50 points To the right of a relative maximum of a continuous function, the curve is _________ (increasing, decreasing, or unable to determine)

22. Maximum/ Minimum – 10 points If the graph of a continuous function changes from increasing to decreasing Then a ____________ has occurred. (maximum, minimum, or unable to determine)

23. Maximum/Minimum– 20 points For a continuous function, If f ‘ (c ) < 0 and f ‘ (c ) > 0 then F (c ) is a _______. (Maximum, minimum, or Unable to determine)

24. Maximum/Minimum – 30 points Use the sign table to state the x value of the maximum point of the continuous function

25. Maximum/Minimum – 40 points State the x values of the continuous curve’s minimums.

26. Maximum/ Minimum – 50 points State the x value of the relative maximum point for the function, Y = 2x3 + 3x2 – 36x