Let $a , b \in \mathbb { R }$ and $f : \mathbb { R } \rightarrow \mathbb { R }$ be defined by $f ( x ) = a \cos \left( \left| x ^ { 3 } - x \right| \right) + b | x | \sin \left( \left| x ^ { 3 } + x \right| \right)$. Then $f$ is (A) differentiable at $x = 0$ if $a = 0$ and $b = 1$ (B) differentiable at $x = 1$ if $a = 1$ and $b = 0$ (C) NOT differentiable at $x = 0$ if $a = 1$ and $b = 0$ (D) NOT differentiable at $x = 1$ if $a = 1$ and $b = 1$
On the coordinate plane, let $\Gamma$ be the graph of the cubic function $f(x) = x^{3} - 9x^{2} + 15x - 4$. Show that $P(1, 3)$ is a point on $\Gamma$, and find the equation of the tangent line $L$ to $\Gamma$ at point $P$.
The tangent line drawn to the graph of the function $y = f ( x )$ at the point $( 2,4 )$ passes through the point $( - 1,3 )$. Accordingly, what is the value of $f ^ { \prime } ( 2 )$? A) $\frac { 1 } { 2 }$ B) $\frac { 5 } { 2 }$ C) $\frac { 1 } { 3 }$ D) $\frac { 4 } { 3 }$ E) $\frac { 3 } { 5 }$