我是小白，请帮我详细一步一步解析上面两道数学题---**Problem 16** (本题满分 15 分) 已知函数 $f(x)=e^x-ax-a^3$. (1) 当 $a=1$ 时, 求曲线 $y=f(x)$ 在点 $(1, f(1))$ 处的切线方程; (2) 若 $f(x)$ 有极小值, 且极小值小于 0, 求 $a$ 的取值范围. **Problem 17** (本题满分 15 分) 如图, 平面四边形 $ABCD$ 中, $AB=8, CD=3, AD=5\sqrt{3}, \angle ADC=90^\circ, \angle BAD=30^\circ$. 点 $E,F$ 满足 $\vec{AE}=\frac{2}{5}\vec{AD}$, $\vec{AF}=\frac{1}{2}\vec{AB}$, 将 $\triangle AEF$ 沿 $EF$ 对折至 $\triangle PEF$, 使得 $PC=4\sqrt{3}$. (1) 证明: $EF \perp PD$; (2) 求面 $PCD$ 与面 $PBF$ 所成二面角的正弦值. **Diagram Description (Accompanying Problem 17):** * Type: 3D geometric figure showing a configuration of points and line segments in space after a folding operation. * Main Elements: * Points: Labeled points A, B, C, D, E, F, P. * Lines: * Solid lines: EF, PB, PC, PD, FB, BC, CD, DE, AE, AF. * Dashed lines: PA, PD (partially dashed). * Shapes: Triangles PEF, PBF, PCD, AEF (before folding, its position is indicated by PEF). Apparent segments forming a quadrilateral ABCD, though A, B, C, D are not coplanar in the 3D view. * Relative Position: Point P is located above the plane containing A, E, F before folding. E is on AD, F is on AB. The figure shows the state after $\triangle AEF$ is folded to $\triangle PEF$ along EF. Points A, E, D appear roughly collinear, and A, F, B appear roughly collinear in the original planar configuration. This completes the extraction.