Find the Value or Values Of $c$ That Satisfy the Equation $\frac { f ( b ) - f ( a ) } { b - a } = f ^ { \prime } ( c )$

question 146

Multiple Choice

Find the value or values of $c$ that satisfy the equation $\frac { f ( b ) - f ( a ) } { b - a } = f ^ { \prime } ( c )$ in the conclusion of the Mean Value Theorem for the function and interval.
- $f ( x ) = x ^ { 2 } + 3 x + 1 , [ - 1,2 ]$

• A) \(0 , \frac { 1 } { 2 }\)
• B) \(- 1,2\)
• C) \(\frac { 1 } { 2 }\)
• D) \(- \frac { 1 } { 2 } , \frac { 1 } { 2 }\)

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Definitions:

Cations

Positively charged ions that have more protons than electrons, playing essential roles in chemical reactions and biological processes.

Ions

Charged particles formed when atoms or molecules gain or lose electrons, playing critical roles in chemical reactions and cellular functions.

High Concentration

A comparative term referring to a scenario in which a particular substance is present in large amounts relative to other substances or relative to its usual amount.

Low Concentration

A condition characterized by a reduced amount of a substance in a given area or volume.