turkey-yks 2025 Q22

turkey-yks · Other · yks-ayt Chain Rule Chain Rule with Composition of Explicit Functions
In the rectangular coordinate plane, for a function $y \geq f(x)$,
  • the tangent line at the point $(2, f(2))$ is $y = 3x - 1$
  • the tangent line at the point $(5, f(5))$ is $y = 2x + 4$

Accordingly, for the function $$g(x) = x^{2} \cdot (f \circ f)(x)$$
what is the value of $g'(2)$?
A) 64 B) 72 C) 80 D) 88 E) 96
In the rectangular coordinate plane, for a function $y \geq f(x)$,

\begin{itemize}
  \item the tangent line at the point $(2, f(2))$ is $y = 3x - 1$
  \item the tangent line at the point $(5, f(5))$ is $y = 2x + 4$
\end{itemize}

Accordingly, for the function
$$g(x) = x^{2} \cdot (f \circ f)(x)$$

what is the value of $g'(2)$?

A) 64
B) 72
C) 80
D) 88
E) 96