Đáp án:
$\begin{array}{l}
c)y = 2\sin x + 3\left( {0 \le x \le \dfrac{{3\pi }}{4}} \right)\\
Do:0 \le x \le 1\,khi\,0 \le x \le \dfrac{{3\pi }}{4}\\
\Rightarrow 3 \le 2\sin x + 3 \le 5\\
\Rightarrow 3 \le y \le 5\\
\Rightarrow \left\{ \begin{array}{l}
GTNN:y = 3\\
\,khi:\sin x = 0 \Rightarrow x = 0\\
GTLN:y = 5\,\\
khi:\sin x = 1 \Rightarrow x = \dfrac{\pi }{2}
\end{array} \right.\\
d)y = 2{\sin ^2}x + 3\sin x + 7\\
= 2\left( {{{\sin }^2}x + 2.\sin x.\dfrac{3}{4} + \dfrac{9}{{16}}} \right) - 2.\dfrac{9}{{16}} + 7\\
= 2.{\left( {\sin x + \dfrac{3}{4}} \right)^2} + \dfrac{{47}}{8} \ge \dfrac{{47}}{8}\\
\Rightarrow GTNN:y = \dfrac{{47}}{8}\\
Khi:\sin x = - \dfrac{3}{4}
\end{array}$
