Assignment:
Q1. Decide whether Rolle’s Theorem can be applied to f(x) = x4 - 4x3 + 4x2 +1 on the interval [-1,3]. If Rolle’s Theorem can be applied, find all the values, c, in the interval such that f'(c) = 0 . If Rolle’s Theorem cannot be applied, state why.
Q2. An open box is to be made from a rectangular piece of material by cutting equal squares from each corner and turning up the sides. Find the dimensions of the box of maximum volume if the material has dimensions 6 inches by 6 inches.
Q3. Describe or sketch (if possible) the graph of the function f(x) = x2 - 4x + 1 / x2 + 1 . You must use the first and second derivative tests and name any intercepts, relative extrema, points of inflection, and asymptotes. Also include any intervals on which the function is increasing or decreasing and any types of concavity.
Provide complete and step by step solution for the question and show calculations and use formulas.