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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