Calculus Critical Points Jeopardy

Graphic Extrema

Derivatives Critical Points Increasing/ Decreasing

Maximum/ Minimum

10 10 10 10 10

20 20 20 20 20

30 30 30 30 30

40 40 40 40 40

50 50 50 50 50

Max/ Min – 10 pointsUse the graph below to state the Absolute Extrema.

Max/Min – 20 pointsState the x values of Relative Maximum.

Max/Min – 30 pointsState the x values of Relative Minimum

Max/Min – 40 pointsState the x values of ALL Relative Extrema.

Max/Min – 50 pointsState the x values of Relative & Absolute Extrema.

Derivative – 10 points

f( x) = x3 – 6x2 + 12x – 5

f( x) = ?? Factored completely!

Derivatives – 20 points

f( x) = 4x2 – 10x + 14f ‘( 4 ) = ?

Derivative – 30 pointsF(x) = 3x4 – 4x3 -36x2

f ’(x) = 0 when x = ???

Derivatives – 40 pointsUse the Chain rule to take derivative.(Factor for additional 20 points)

Y = (2x3 – 6x2 ) 4

Y ‘ = ?

Derivatives – 50 pointsCalculate and simplify the derivative.

Critical Points – 10 points

State the critical point of f(x) = 4x2 – 16x - 12

Critical Points – 20 points

State the 2 critical points of

f(x) = x3 – 12x + 7

Critical Points – 30 points

State the 2 critical points of f(x) = 2x3 + 3x2 – 12x + 8

Critical Points – 40 points

State the critical points of f(x) = x4 – 2x2 + 1

Critical Points – 50 points

State the critical points of f(x) = 3x4 + 16x3 + 18x2 - 12

Increasing/ Decreasing – 10 pointsFor the curve below state the decreasing intervals

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

Increasing/ Decreasing – 30 points

Use the sign table below to state the Increasing intervals.

Increasing/ Decreasing – 40 points

f( x) = x3 + 3x2 + 4State the decreasing interval

Increasing/Decreasing – 50 points

To the right of a relative maximum of a continuous function, the curve is_________ (increasing, decreasing, or unable to determine)

Maximum/ Minimum – 10 points

If the graph of a continuous function changes from increasing to decreasingThen a ____________ has occurred.(maximum, minimum, or unable to determine)

Maximum/Minimum– 20 points

For a continuous function,If f ‘ (c ) < 0 and f ‘ (c ) > 0 thenF (c ) is a _______.(Maximum, minimum, or Unable to determine)

Maximum/Minimum – 30 points

Use the sign table to state the x value ofthe maximum point of the continuous function

Maximum/Minimum – 40 points

State the x values of the continuouscurve’s minimums.

Maximum/ Minimum – 50 points

State the x value of the relative maximumpoint for the function,

Y = 2x3 + 3x2 – 36x