2) For $0 \leq x \leq 6$, find the coordinates of the points of intersection of the curves $y=x^{2} \cos x$ and $x+2 y=1$.
Answer
\(\boxed{\text{Final Answer: The points of intersection of the curves are approximately }(0.524, 0.238)\text{ and }(4.628, -1.814)}\)
Step 1 ：Rewrite the second equation in terms of y: \(y = \frac{1 - x}{2}\)
Step 2 ：Set the two equations equal to each other: \(x^2 \cos x = \frac{1 - x}{2}\)
Step 3 ：Use a numerical solver to find the x values where the two curves intersect: \(x \approx 0.524\) and \(x \approx 4.628\)
Step 4 ：Plug the x values back into either equation to find the corresponding y values: \(y \approx 0.238\) and \(y \approx -1.814\)
Step 5 ：\(\boxed{\text{Final Answer: The points of intersection of the curves are approximately }(0.524, 0.238)\text{ and }(4.628, -1.814)}\)
