Find the Intervals on Which the Function Is Increasing and the Intervals

question 143

Multiple Choice

Find the intervals on which the function is increasing and the intervals on which the function is decreasing.
- $$f ( x ) = x ^ { 2 } - 5 x + 6$$

• A) Increasing on \(\left( \frac { 5 } { 2 } , \infty \right)\); decreasing on \(\left( - \infty , \frac { 5 } { 2 } \right)\)
• B) Increasing on \(\left( - \frac { 5 } { 2 } , \infty \right) ;\) decreasing on \(\left( - \infty , - \frac { 5 } { 2 } \right)\)
• C) Increasing on \(\left( - \infty , - \frac { 5 } { 2 } \right) ;\) decreasing on \(\left( - \frac { 5 } { 2 } , \infty \right)\)
• D) Increasing on \(\left( - \infty , \frac { 5 } { 2 } \right)\); decreasing on \(\left( \frac { 5 } { 2 } , \infty \right)\)

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Definitions:

Independent Events

Describes two events where the occurrence of one does not affect the probability of the occurrence of the other.

Conditional Probability

The odds of an event taking place assuming another distinct event has occurred previously.

Joint Probability

The probability of two or more events happening at the same time, assuming there is some relationship between the events.

Complement Rule

A principle in probability theory stating that the probability of the complement of an event equals one minus the probability of the event itself.