1. Estimate the zero of () = 3³ + 5² + 2 + 1 using Newton's method with three iterations starting at ₁ = 1. Use graphing technology to determine the value of the zero, and show the error between the estimated value and the graphed value.

2. Let be a twice-differentiable function with (1) = 7 and (7) = 1 and let () = (()). a) Justify why there must be a value , where 1 < < 7, such that () = 1.

b) Justify that (1) = (7) and that there exists a value such that on (1,7) where () = 0.

3. Consider the function () = ³ 4 + 2.

a) Determine the absolute minimum and absolute maximum of () over the interval [1, 2]. b) Does your answer change if the interval is (1, 2)? Explain.