Rate of Change, Intervals of Inc/Dec, Concavity

Organize these options into the right categories.

Groups:

(a) Function is increasing

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(b) Function is decreasing

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Organize these options into the right categories.

Groups:

(a) Function is concave up.

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(b) Function is concave down.

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Organize these options into the right categories.

(Must remember cold... ROC is increasing -> concave up)

Groups:

(a) The ROC is increasing.

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(b) The ROC is decreasing.

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Match each graph to the correct description.

Remember:

If the ROC of f is positive -> f increases

If the ROC of f is increasing -> f is concave up

• The ROC is positive and decreasing.

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• The ROC is negative and increasing.

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• The ROC is positive and increasing.

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• The ROC is negative and decreasing.

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The extrema for the graph of f and the point of inflection of the graph of f are labeled where A, B, C, D, and E represent the x-coordinates at those points.

On which interval is f increasing at an increasing rate?

• the interval from A to B

• the interval from B to C

• the interval from C to D

• the interval from D to E

The extrema for the graph of f and the point of inflection of the graph of f are labeled where A, B, C, D, and E represent the x-coordinates at those points.

On which interval is f decreasing and the graph of f concave up?

• the interval from A to B

• the interval from B to C

• the interval from C to D

• the interval from D to E

The extrema for the graph of f and the point of inflection of the graph of f are labeled where A, B, C, D, and E represent the x-coordinates at those points.

Which statement and explanation is correct concerning the interval from C to D?

• On the interval from C to D, the graph of f is increasing because the graph of f is concave down.

• On the interval from C to D, the graph of f is increasing because the rate of change of f is increasing.

• On the interval from C to D, the graph of f is increasing because the rate of change of f is positive.

• On the interval from C to D, the graph of f is increasing because the rate of change of f is linear.

The extrema for the graph of f and the point of inflection of the graph of f are labeled where A, B, C, D, and E represent the x-coordinates at those points.

Which statement and explanation is correct concerning the interval from A to B?

• On the interval from A to B, the graph of f is concave up because the rate of change of f is negative.

• On the interval from A to B, the graph of f is concave up because the rate of change of f is increasing.

• On the interval from A to B, the graph of f is concave down because the rate of change of f is increasing.

• On the interval from A to B, the graph of f is concave down because the rate of change of f is negative.

The extrema for the graph of f and the point of inflection of the graph of f are labeled where A, B, C, D, and E represent the x-coordinates at those points.

On which interval is the rate of change of f negative and decreasing?

• the interval from A to B

• the interval from B to C

• the interval from C to D

• the interval from D to E

Select the description that best matches the graph of function k shown here.

• k is decreasing at an increasing rate

• k is increasing at an increasing rate

• k is decreasing at a decreasing rate

• k is increasing at a decreasing rate