120- At the intersection points of the curves $f(x) = \sin x + \dfrac{1}{2}\cos x$ and $g(x) = \dfrac{3}{2}\sin x$ on the interval $[0, \pi]$, a tangent line to the curve $f(x)$ is drawn. This tangent line intersects the $x$-axis at which interval? (1) $\dfrac{\pi}{4} - 1$ (2) $\dfrac{\pi}{4} - 2$ (3) $\dfrac{\pi}{4} + \dfrac{1}{\lambda}$ (4) $\dfrac{\pi}{4} + \dfrac{3}{\lambda}$ %% Page 6 121-- Function $f$ is differentiable and periodic with period 5. If $f'(-1)=\dfrac{3}{2}$ and $g(x)=f(x+1)+f(3x+10)$, then $g'(-2)$ is which of the following? (1) $3$ (2) $\dfrac{7}{2}$ (3) $6$ (4) $\dfrac{13}{2}$
\textbf{120-} At the intersection points of the curves $f(x) = \sin x + \dfrac{1}{2}\cos x$ and $g(x) = \dfrac{3}{2}\sin x$ on the interval $[0, \pi]$, a tangent line to the curve $f(x)$ is drawn. This tangent line intersects the $x$-axis at which interval?
\medskip
(1) $\dfrac{\pi}{4} - 1$ \hfill (2) $\dfrac{\pi}{4} - 2$ \hfill (3) $\dfrac{\pi}{4} + \dfrac{1}{\lambda}$ \hfill (4) $\dfrac{\pi}{4} + \dfrac{3}{\lambda}$
%% Page 6
\textbf{121--} Function $f$ is differentiable and periodic with period 5. If $f'(-1)=\dfrac{3}{2}$ and $g(x)=f(x+1)+f(3x+10)$, then $g'(-2)$ is which of the following?
\medskip
(1) $3$ \hfill (2) $\dfrac{7}{2}$ \hfill (3) $6$ \hfill (4) $\dfrac{13}{2}$
\bigskip