Find the Absolute Extreme Values of the Function on the Interval

question 165

Multiple Choice

Find the absolute extreme values of the function on the interval.
- $$g ( x ) = - x ^ { 2 } + 7 x - 12,4 \leq x \leq 3$$

• A) absolute maximum is \(\frac { 1 } { 4 }\) at \(x = \frac { 9 } { 2 } ;\) absolute minimum is 0 at 3 and 0 at \(x = 4\)
• B) absolute maximum is \(\frac { 97 } { 4 }\) at \(x = \frac { 7 } { 2 }\); absolute minimum is 0 at 3 and 0 at \(x = 4\)
• C) absolute maximum is \(\frac { 1 } { 4 }\) at \(x = \frac { 7 } { 2 }\); absolute minimum is 0 at 3 and 0 at \(x = 4\)
• D) absolute maximum is \(\frac { 5 } { 4 }\) at \(x = \frac { 9 } { 2 }\); absolute minimum is 0 at 3 and 0 at \(x = 4\)

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Definitions:

Excessive Drinking

The consumption of alcohol in amounts that are harmful to one's health or lead to behavior that is damaging to oneself or others.

Alcoholism

A chronic condition characterized by uncontrolled drinking and a preoccupation with alcohol, despite adverse effects.

Drinking Alcohol

The consumption of beverages containing ethanol, which can have various social, cultural, and physiological effects.

Pre-smoking Levels

Baseline levels of physiological or psychological measures before an individual starts smoking.