Determine Whether the Mean Value Theorem Can Be Applied to the Function

question 137

Multiple Choice

Determine whether the Mean Value Theorem can be applied to the function $f ( x ) = x ^ { 2 }$ on the closed interval $[ 3,9 ]$ . If the Mean Value Theorem can be applied, find all numbers $c$ in the open interval $( 3,9 )$ such that $f ^ { t} ( c ) = \frac { f ( 9 ) - f ( 3 ) } { 9 - ( 3 ) }$ .

• A) MVT applies; \(c = 6\)
• B) MVT applies; \(c = 7\)
• C) MVT applies; \(c = 4\)
• D) MVT applies; \(\mathrm { c } = 5\)
• E) MVT applies; \(c = 8\)

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Definitions:

Independent Variable

A variable that is manipulated or changed in an experiment to see if it has an effect on the dependent variable.

Correlation Coefficient

A statistical measure that indicates the extent to which two or more variables fluctuate together, ranging from -1 to 1, where 1 means a perfect positive relationship, -1 means a perfect negative relationship, and 0 means no relationship.

Variables

Elements or factors that can change and affect the outcomes of scientific research or experiments.

Correlation Coefficient

A statistical measure that indicates the extent to which two variables fluctuate together, showing the strength and direction of their relationship.