Consider the Function $f ( x ) = x ^ { 2 }$

Consider the function $f ( x ) = x ^ { 2 }$ on the interval $\left[ 0 , \frac { 1 } { 2 } \right]$ . According to the Mean Value Theorem, there must be a number c in $\left( 0 , \frac { 1 } { 2 } \right)$ such that $f ^ { \prime } ( c )$ is equal to a particular value d. What is d?

A) $\frac { 3 } { 2 }$

B) 1
C) $\frac { 1 } { 2 }$
D) 2
E) $\frac { 2 } { 3 }$
F) $\frac { 3 } { 4 }$

G) $\frac { 1 } { 4 }$

H) 3

Correct Answer:

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