The slope of the tangent line to the graph of a function f at $\mathrm { x } = \mathrm { a }$ is $1$, and the slope of the tangent line at $x = b$ is $\sqrt { 3 }$. Given that the second derivative function $\mathbf { f } ^ { \prime \prime } ( \mathbf { x } )$ is continuous on the interval $[ \mathbf { a } , \mathbf { b } ]$, what is the value of $$\int _ { b } ^ { a } f ^ { \prime } ( x ) \cdot f ^ { \prime \prime } ( x ) d x$$ ? A) - 1 B) 1 C) 2 D) $\frac { 1 } { 3 }$ E) $\frac { 2 } { 3 }$
The slope of the tangent line to the graph of a function f at $\mathrm { x } = \mathrm { a }$ is $1$, and the slope of the tangent line at $x = b$ is $\sqrt { 3 }$.\\
Given that the second derivative function $\mathbf { f } ^ { \prime \prime } ( \mathbf { x } )$ is continuous on the interval $[ \mathbf { a } , \mathbf { b } ]$, what is the value of
$$\int _ { b } ^ { a } f ^ { \prime } ( x ) \cdot f ^ { \prime \prime } ( x ) d x$$
?\\
A) - 1\\
B) 1\\
C) 2\\
D) $\frac { 1 } { 3 }$\\
E) $\frac { 2 } { 3 }$